Can you solve the puzzle that's dividing the internet?
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- Опубликовано: 18 май 2024
- What's the answer? A book costs $1 plus half its price. How much does it cost? Nearly 40% of people are not able to solve for the answer.
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Obvious fact: everything costs two halves its price. If the book costs $1 plus one half its price, then $1 must be the other half. So the book costs 2 × $1, or $2.
that is the correct logic for this.
@@GraveUypo That's definitely how I found the answer.
Exactly 💯
Noice! 👍
That actually helps a lot for me understanding this. Originally I was confused and got the wrong answer, because I was like "well you could set the price to anything you want, so telling me it's half the price +1 doesn't tell me much" but this clears that up.
I think people said it can't be answered because of recursion, rather than price vs cost. Starting with $1, the price becomes $1.50. But half of that is 0.75, so the price becomes $1.75. But half of that is 0.88, so it becomes $1.88. And then they give up.
1 + the sum of 1/(2^n) as n goes to infinity
An infinite number of mathematicians walk into a bar. The first says, I'll have one pint of beer please. The second says, I'll have half a pint of beer please. The third says, I'll have a quarter pint please. The fourth asks for 1/8th pint. Etc.
The barman pours two pints and says "you guys really ought to know your limits"
@@plotted_pant42 Which, luckily enough, converges at 2 (which is also the actual answer).
@@Stratelier Because of the semantic confusion, i have trouble determining whether or not this is a coincidence
@@xereetoAfter a good drink they all return to their infinite hotel, but the recepcionist says infinitely many new guests have arrived and everyone needs to move into a new room.
Working backwards from the answer.. it's much easier to see what the question is actually asking. The answer is actually right there in the question. "one dollar plus half the cost" -- literally implies that the $1 is the 'other half of the cost.
Thats a good way to look at it
I had the same thought! Honestly, internet just loves to argue over the dumbest things.
Yeah I thought the price and cost were 2 different variables, and that the $1 was an additional fee not factored into the price, it's a poorly phrased question. im so used to hidden fees in capitalism I thought thats what it was
But it is not correct. Price= sticker price. Cost = what you pay.
@@charlesspringer4709 In a world with taxes.. You're right.
I read it from the view of the seller that bought a book for $1 and wants to resell it but wants to have a profit margin of 50%. So the answer would be $1.50 in this case
Regarding the cost vs price thing, I would add that cost meaning price isn't just via usage or peculiarities of definition, but rather a matter of perspective. The cost of a book to create, and the cost for me to acquire it. The cost for me to acquire the already made book would be the price of the book. The book cost me $2. That was the cost _to me_ . Here, cost and price, which are themselves different things, come into alignment.
The cost to me is the price of the book.
From the perspective of the publisher, the cost will be different. (rights, price of printing, marketing, etc...)
From the perspective of the printer, the cost will be different. (materials, labor, machinery, etc...)
From the perspective of the writer, the cost will be different. (time, living expenses while writing, payables for research, failed marriage, etc...)
etc...
The fact that cost and price are nuanced but that the seller intended a more generic meaning of the word means that it is a poorly worded question. The reader cannot, without context, be expected to ignore what they know about cost and price and reliably use the intended definition.
I would say in most places, the price is $2 but the cost to you is $2 + tax…
Wait, this video is over 8 minutes long. Really curious how that question is going to get stretched.
Taking very slowly with weird long pauses between each sentence. I had to watch 1.5x
@@OmnipotentO You should have watched at 2x, 1.5 is the wrong answer.
@@FlyingFox86 LOL
@@FlyingFox86 haha, very clever
NEED THE 8 MINS 🤑🤑🤑🤑
Seen it in other wording in another soviet math puzzles book: "A brick weighs half a kilo and half a brick. How much does a brick weigh?". The puzzle itself must be even older than that, because someone had to know it before putting into the book.
Yeah this is a much better wording.
It seems like a lot of the controversy of these viral internet questions stems from them being poorly worded. I understood this one much better.
I understand the answer in terms of how you are asking the question but I can also see how some answers were "the value cannot be determined". It you take the question to ask A book costs ($1 + (1/2Price of Book)) the price of the book may be $10, in which case the buyer is getting a deal by paying $6.00. In this case the value for the cost of the book could not be determined as asked by the question. I think the question could be considered semantically ambiguous.
I think you missed the biggest possibility of why people were choosing "the value cannot be determined". In your presented formula of b = 1 + b/2, you make the assumption that price and cost are not only interchangeable but are in fact equal to each other. Other people are seeing those as two different variables, meaning they are trying to solve the equation as c = 1 + p/2, where c is the calculated Cost of the book and p is the *known* Price of the book. In that situation, the problem does not present enough information to solve as both c and p are unknown values.
You just gave an example of someone who overthinks the problem!!
We are clearly meant to assume they are equal
It is so easy to determine that half of a book's price is equal to half of the damn book's price. The reason why the whole and half are in the equation is for you to be able to solve the damn problem. Those who make 2 different variables obviously forgot how and when should you use these variables. We have variable b to account for the WHOLE price, and the half of the price was mentioned so that would be the half of b. It is not an assumption made by this RUclipsr but it is an obvious rule in solving algebraic expressions that when you have a given and half a given then they'd of course correspond and be b and b/2
Some of this depends on your life experience. Many will just assume (remember the 'when you assume you make an ass out of you and me') that price and cost are the same thing...but anyone with business experience KNOWS that price and cost are NEVER the same thing so you have an unknown variable in the question that cannot be answered. You can't say that this thinking is wrong...because technically it is MORE correct than assuming that cost and price are equal despite them being synonyms in the dictionary.
@@recoilrob324 the price of a book is the cost of a book if you are buying it, sure for a corporation there’s a difference, shipping, tax, storage, and other things must be considered, but for a consumer it’s not two different things
The problem is that a book has three values attached that are commonly referred to as its cost. Its actual retail price, its MSRP (manufacturer suggested retail price), and its COGS (cost of goods sold, what they paid to acquire it).
Without specifying which if these three prices is referred to, there is not enough information in the question.
Illustrating this, the video simplifies the statement to x=1+x/2, but that only applies if we make the assumption that cost refers to its actual retail price, otherwise saying x=y in y=1+x/2 is not justified
If you speak English you should be able to understand what the question is trying to ask you. It’s not a trick question
@@koibubbles3302 You're specifically trained in mathematics to look for situations where you do not have enough information.
@@shadeblackwolf1508 overinterpreting the wording of a question is not mathematical in nature
@@shadeblackwolf1508 you could just as easily argue that “it” wasn’t defined, and that this ambiguous entity prevents you from answering the question. You have to learn how to make reasonable assumptions, so long as you’re open to the possibility that the assumption you made was wrong. If you can’t do that, that’s on you. Not the question.
1. A book costs something. How much does the book cost?
2. A book costs (half its price). How much does the boom cost?
3. A book costs (half its price plus half its price). How much does the book cost?
4. A book costs (something plus half its price). How much does the book cost?
5. A book costs ($1 plus half its price). How much does the book cost?
6. A book costs ($2 off plus half its price). How much does the book cost?
General form of the equation
c = book costs something
costs and price are synonyms.
x = something
c = x + c/2
Substituting for x, for
1. c = x
2. c = c/2
3. c = c/2 + c/2
4. c = x + c/2
5. c = 1 + c/2
6. c = -2 + c/2
We end up with absurdities if x is equal to or less than 0.
Either c = c/2 (where x = 0) or the "discount" doubles.
While it's a reasonable assumption that costs is a transitive verb, costs and price are synonyms, its not the only reasonable assumption. Other reasonable assumptions, are price is one part of how much a book costs, other parts (from the consumer POV) being taxes and fees, additional discounts.
While the intended answer is $2, the way the problem is formed ignores basic realities of how commerce is conducted and what things add to or subtract from the price/cost of an item, or even that something could be on sale, i.e. 2 for 1 (1 item costs half its price), or a 50% off sale (half its price).
There's simply not enough information to know if
1) $1 is in addition to half its (unknown) price; or
2) $1 is the cost/price of the book and half its price is the sales tax, resulting in $1.50; or
3) $1 plus half its price/cost (c = 1 + c/2), resulting in $2; or
4) the book costs $1, full stop, the additional half its price is meaningless, its not asking for the total cost, price + taxes + fees + discounts. Only the cost of the book.
The above is no more overthinking it, than grammar lessons on transitive verbs and cost/price as synonyms to dismiss cost and price being two different things.
It's free!
Someone has taken overthinking this problem to a level I didn't want to even consider as soon as I saw how long the comment was!! 🙄
@@michaeldeierhoi4096it wasn't overthinking anymore than the videos overthinking to dismiss cost v. price.
The short version: how much something costs includes, but is not limited to its price, taxes, discounts, fees, gratuities, and shipping.
Does the book cost $1 (price) plus half its price (a 50% tax)?
Does the book cost $1 (fee) plus half its price (a 50% discount)?
Does cost = price? Does cost ≠ price?
The only thing that you can say for certain is that the cost of the book is $1 more than half its (unknown) price.
It can be true that the question came from an old textbook, AND that the question was written to be confusing. There's a reason it was written in this way, and not "What is 1 + 0.5*2". To confuse people.
the true answer is that the statement is too ambigious and poorly worded
The irritating thing about word problems is when you have to make an educated guess because of ambiguity in the wording that may or may not be deliberate. While I came up with the majority answer, to a businessman the difference between the cost of something and its price is the profit margin.
If a merchant purchases something (the cost) for resale (the price) and wants to make a profit margin of 20%, you multiply the cost x 1.25. The formula for the establishing the selling price of something that costs a given amount is to multiply the cost x 1/(1-M). M is the profit margin expressed as a decimal. Thus, in the example given above, the cost is multiplied by (1/1-.2) = 1/.8 =10/8 = 5/4 =1.25. The profit margin is defined to be what percentage of the SELLING PRICE is your profit.
THE COST (as a noun) is never used in the riddle. "How much does it cost?" cost is also a verb here and therefore can't be confused with the cost of producing it.
Just like: How much does it weigh? - > does weigh = verb
What is its weight? - > weight = noun
I think part of the problem is that the question sounds like nonsense. It could have something to do with the wording, alternating between price and cost. It almost makes it sound like those are two different things, like the cost to produce it versus the price to buy it.
Kind of dependent on how you define price and cost. To an end consumer, they're more or less the same thing. "The price is $2, so it costs me $2 to buy it." Not necessarily the case for someone along the chain of its manufacture.
And that's just the way it's defined in my part of the US. I would absolutely believe that there are places in the English-speaking world where the local vernacular draws a hard line between "price" and "cost".
It reads perfectly well. The problem is that literacy is on the sharp decline.
It reads perfectly fine to a 3rd grader for the answer given, to a college educated CPA, it also reads fine, resulting in a different answer.
@@ianmalcolm2552 The 3rd grader has more common sense. The problem is wrote specifically, and the mixing up of definitions could only be done by someone in finance... Charlatans of logic.
@aperinich, do a search on “cost vs price” you’ll be enlightened.
0:14 easy, E (it is a value that approaches infinity over time)
who liked?
I respectfully disagree, as a retailer, cost is totally different than price. Price is what you sell it for and cost is what it costs you, the seller. You should not have to jump to a conclusion that cost means price to get the answer. Poorly written question.
But the question never uses "cost" as a noun, only as a verb.
That doesn’t matter, if you look at it from the sellers point, it costs them x amount and is priced at y. The verbiage should have used one term, cost, or not had cannot be determined as an option for the answer.
@@Steve_Stowers That's reaching. The question is specifically worded in a tricky way, and the noun and the verb versions of "cost" have multiple meanings.
That's the fundamental problem with most of these "questions." They are a word trick rather than a math problem. And the solution relies on using the meaning the author wants you to use. To me, cost and price are two different things.
The price is the buyers cost.
The equation you used at the beginning is not correct.
If the book cost $1 plus half its cost, then the problem should be written that way. It is not.
ergo: cost = 1 + (price/2)
Even using your own logic, let's say the book is priced at $10, the cost of the book is $6, ergo, the cost is still less than the price.
Arbitrarily saying cost=price is no different to saying cost = 10 or price = 20 or any other arbitrary values.
And even if we presume price and cost are interchangeable terms, it's not impossible to presume that the price is the price plus some additional amount (perhaps tax, shipping, or whatever) that amounts to half again the price, as presented in this example.
If a book is priced/costed at $1 plus tax (some fraction of its price, arbitrarily half in the word problem), then the book costs $1.50 for the purposes of the word problem when read as printed.
The entire problem could be disambiguated and solve the issue. There's no reason to assume cost = price when we're told cost = 1 + (price/2)
This is like complaining to a physics teacher why they aren't accounting for air resistance.
@@baldwinplayz268 No, the cost is the object, and the price is the subject, I think. They're functionally two different thing the way the sentence is written.
the question is worded confusingly, but the original answer was meant to be 2 because it was meant to be interpreted as x = 1 + x/2. x is the actual price and its value is 1 + half of the actual price, which is also 1. his equation is not incorrect
That's why the book is free!
He quite literally addresses this IN THE VIDEO. Did you even watch to the end?
But regardless of that, I think this is an incredibly silly objection. Imagine someone said "The distance between X and Y is 12m, and the distance between Y and Z is 18m. Assuming X, Y, and Z all lie on a line with Y in the middle, what is the length between X and Z?" and someone responded by saying that the question is impossible because "distance" is not the same word as "length." Any sane person reading this would understand that they both mean the same thing in this context, and although someone COULD define them differently (e.g. straight-line distance versus geodesic length), they should be interpreted the same in this question.
$2, ez, you just lost a customer, and I saved 8 minutes of my time
Assuming straight math, the answer is pretty obviously $2.
X = X/2 + X/2
X = X/2 + 1
X/2 = 1
X = 1 + 1
X = 2
The thing is, that second step assumes that the book is being sold for its normal price. If a special deal is going on, it would be something like
Y = X/2 + 1
And now we no longer have a way to determine X, and per extension no way to determine Y, at least not with the given information. If we say that the normal price of the book is 4$, for example, that means that the current price is
Y = X/2 + 1
X = 4
X/2 = 2
Y = 2 + 1
Y = 3
TL;DR: If we assume a straight math question, the answer is 2. If we apply real world situations, the answer is "too little information." Which is the major downfall when trying to make a math question into a story; the moment you make it into a real-world situation, people are going to apply real-world logic to it.
There's probably a large capture of "just show me the answer" people in the "can't be determined" option.
If the price of the book is listed as $12 and the store is having a sale for $1+half listed price, that would be $7.
The original question is ambiguous.
$1 can be interpreted as a fee based on this wording. For example, Ticket Master has a particular event on sale for half off. When you check out, there's TM's $1 fee + the sale price of the ticket. We don't know the non-sale price of the event, therefore we don't know what the final checkout price will be based on the question.
I'm having the problem that I'm thinking this in terms of a real-world situation or more like a developer mind-set, where a bookstore is selling a book with price X, as X / 2 + $1, where X is definitely not a value that can be determined because it could be anything. Your solution implies a "calculation of the starting price of a book" let's say, where my starting point is that "the book has already a price, but I'm selling it at half its price plus $1".
The difference is something like:
Value = 1 + Value / 2
Versus:
NewValue = 1 + OldValue / 2
And I'm blaming the phrasing of the problem (?
Ask an accountant, they will say that you are absolutely correct 👍
I'm also damaged from too many math lectures and started to find the limit to a series: b = 1 + 1/2 + 3/4 + 5/8 + ...
I'm also damaged by programming all day. My brain thinks that an equals sign after (or before) a variable must mean that it's declaring the value of the variable, rather than it just being a regular boolean operation, where we have to figure out what b is.
My brain goes to overhearing a conversation, where you missed part of it.
Person A: I bought the book at half price.
Person B: Oh? I missed the sale, so I paid a dollar more than that.
You: How much should I expect to pay for the book myself?
The problem with most coding syntax is that equality and assignment are conflated. In Java x=1 means x is assigned the value of 1. It does not assert equality between x and 1 merely declare it so.
Did you make the music that plays at the end of your videos? Is it, like, your theme song or something? Because I was very surprised when I heard the MindYourDecisions theme song in some training videos the company I work at had me watch that were definitely not related to MindYourDecisions.
4:52 I have this book, but it cost more than $2.
😆
Must be inflation or something
tbh i would buy one, i like really simple puzzles
My dad had it when I was a kid
I bought this book when it was $2…now it’s $1…this seems more like a vocab test…I see less math here and more word play…
This question has 3 correct answers depending on your job/perspective - and THAT is why its interesting.
Mathematician: 2
Accountant: 1.50 (and the .50 is TAX)
Engineer/Coder: Edge Case - recursive error, potential infinite recursion.
Its a genuinely interesting question, I was one of those folks that ticked the 'cannot be defined' choice (in the recent poll), because from an engineering and coding solution you are looking at a variable that is defined as a formula of itself: ie it is recursive, Ie the cost is approaching infinity - and a definition of a variable such as this is something to keep an eye out for as it is a known source of bugs. For me to get the same answer as a mathematician the question would have to specify the COST as being DIFFERENT from the ORIGINAL COST, ie the 2 variables would have to have different names. I completely understand the mathematicians perspective on this - Im just here to point out its not the only valid one.
While all 3 jobs are reliant on maths, we all all interpret certain things differently - and that is correct for our different professions, because each profession comes with certain standards and expectations.
In my career this is a prime example of something I would HAVE TO DOUBLE CHECK with the client, to make sure Im getting the correct formula and calculation, and in most real world cases - the answer would be 1.50 as intended by said client, because they exist in a world of business and accounts.
Well the coder should have studied more math because the recursion he would code, would be an infinite recursion but the "final" value would funnily enough be 2. It would be a geometric series which does equal to 2.
@@TheJinjitsu nope I see where your coming from but nope - look at it from a maths 'series' recursion yes, trends to 2... in code It trends to infinity, but much more importantly its an infinite recursion.. ie a 'crash',
How on Earth are people having problems with "An object costs X plus half it's price. What is its price?"
"I'm never going to use this"
Because people misinterpret it. Kinda like a reverse offer, where instead of 30% off, it is the cost (£1), plus 50% of the price (50p), or 50% on top. Obviously it is £2 but I'm surprised this reasoning wasn't covered. Also monetization etc.
Because, if cost and price means the same, then that might mean X + X/2, which would be 1.5 in this case. IE difference between the whole price vs just price. IE an object costs $1 and half of that ($0.5).
We're so used to trick math questions on the internet that people are looking for the trick. If you're not expecting a trick, assuming price and cost are the same thing makes sense, but if you're looking for a trick, that's an obvious one.
I don't know how people are having problems with this.
I am strongly in the opinion that 2$ is the correct answer, however, in some places in the world, for some goods, the "price" of the thing is marketed as the price excluding taxes. So, if a book is marketed with the price (excluding tax) at 1$, this could be argued to be the actual price of the book. However, the actual final cost including tax would be higher. Therefore, to say "the book costs 1$ plus half its cost" could in such a situation be interpreted as "the book costs 1$ (excluding tax), plus half its cost (in tax)", giving a reasonable conclusion that the total cost is 1.5$. Still, I stand by my original statement that 2$ is the correct answer.
There is another possible rationale for "the value cannot be determined"; not that I agree with it but here it goes: on one hand it says "the book costs $1" but it also says that "the book costs $1 plus half its price" which is a contradiction so the price is not properly stated. This is actually what happens when people reply $1.5 but for some reason they don't notice it. If they get to $1.5 it's because they took price=$1 as truth but if then they add the half of $1, which means they didn't notice that they were taking two contradicting truths at the same time. Source: it happened to me when I read this problem as a kid.
Denial: $1.50
Anger: it can’t be solved
Bargaining: let’s just test it to make sure
Depression: tempted to just click on the video to find out
Acceptance: $2
Oh mate. I listened all the way through, but even after that we disagree on that 'indeterminate value' thing. I'm with those who say "Yup, the cost is $1 plus half the price, but as you've not specified the price, the end result is indeterminable." :)
But how can the price be anything else than $2? If it is anything else, then $1 wouldn't be half of it.
@@FlyingFox86 Nope, to me! The actual PRICE could be 2 cents. Then the COST would be $1 plus (2 cents)/2. I don't see that we have any way of knowing the 'answer' from the info given unless we accept his argument that the price == cost, which is not a given here. Happy to be shown wrong, but this one may run and run!
@@BytebroUK When you want to know the price of something in a shop, don't you ever use the phrase "how much does it cost?"
@@FlyingFox86 I have rarely heard anyone in a store ever asking "What is the price of X?" instead of "What does X cost?". And when they ask the latter, no one misunderstands and instead gets into a pedantic lecture of the difference of "cost" versus "price". In fact, whenever someone does use "cost" that way, they almost always specify that they aren't using "cost" as a synonym for "price" because it's recognized that in common usage the two are synonyms. Anyone who smugly goes on about them being different in an everyday context is just being an ass.
It says "half *its* price". Not "half *the*price". A subtle, but important difference. As a result, there's no unknown: it is written that $1 is one half of its price and you need to find the total price.
The internet might not make you smarter, but could help some feel smarter when looking at others' wrong answers.
Look at from the perspective of a bookstore. The bookstore buys a book _at cost._ It sells a book _at price._ So _c = 1 + 1/2 p._ So we have a function of cost and price. If the book is sold at $2 the bookstore breaks even. That's all. The extra cost for the bookstore due to the higher price might be royalty due to the author, for instance.
I don't know how anyone can argue with this. Cost is not always price, depending on context, and this makes the question ambiguous and unanswerable.
Did you record with a $2 microphone for this specific video? Why is your audio so different in this one?
I have to point out that in the question, the word "cost" is used as a verb in both instances. Not once does the question even reference the cost (noun) of the book so the argument of cost vs price makes even less sense. I solved this problem the same way you did but I did the times 2 first then subtracted B from both sides. Still gave me B=2.
I'm glad I wasn't the only one confused about his little speech about the various meanings of 'cost' (the noun) when it doesn't even appear anywhere in the question.
Hallelujah, I found my peers. I was utterly shocked to see that NOBODY in the comment section seemed to have noticed that. But here we are shaking our heads at their ignorance and Presh's mistake. Greetings from a non-native speaker from 🇩🇪
So the origin of confusion is most probably a translation inaccuracy? Because the original wording did not mention price, only cost (both verb and noun):
За книгу заплатили 1 рубль и еще половину стоимости книги. Сколько стоит книга?
For the book was paid 1 rouble and half of the book's cost more. How much does the book cost?
I'm curious to know whether the Russian version uses the same word for price/cost or not!
The Moscow Puzzles! I knew I've seen this puzzle before. I still own it. Lovely book, an absolute classic. Highly recommended. 😊
Let the cost of the book be 'x'
According to condition:
x=1+0.5x
0.5x=1
x=2
Therefore the book costs 2 dollars.
Half it's price not cost, therefore you cannot associate cost and price in the same variable.
@@axel3689 isn't cost and price the same thing?
tranlated from russian and you're assuming it was translated correctly? why would they use two different words to mean the same thing - concept (if i understand the argument right) . why not just use the same word?
your math and answer is right given your assumption, but not if otherwise.
6:21.
x = 1 + 0,5x
0,5x = 1
x = $2
What an interesting puzzle.
I just think the sentence was translated into English and we should check the Russian that is for sure more clear... up to then for me this question is non sensical. Still interesting to see how a mathematical approach handles it.
A small thing but in the previous poll the sample size was 81K and the in the latter one it was 38K. So while looking at the percentages it would seem like there is some improvement, a single percent for the latter poll is less number of people that that for the previous poll. But I understand we can't always have ideal situations and we have to make do with what we have.
I got the two dollar answer. Having looked at the wording more closely, I believe that the indeterminable answer is correct. The way the different words are used could easily denote a difference between the words 'cost' and 'price' rather than those words being interchangeable.
Finally someone with common sense.
What a legend!
Love your style 🤗
I feel your answer depends on your understanding of the question
I think its 2 also, but many people think of "plus its cost" as a form of tax, and you don't add taxes onto the tax
I can not get to your answer from here at the book store. I'm trying to buy it for $2 and they say no. They say the price of the book is the sticker price. The cost to me at the cash register is half the price plus a dollar. They convinced me that is the answer: Half the price plus a dollar. You have to know the stocker price to produce a number.
Go argue with the book sellers. (Russians had no sticker prices. Price varied with your Party association.)
Question is too simple to use algebra, but you also can
1 + x/2 = x
(Multiply for 2) 2 + x = 2x
2 = 2x - x
2 = x
Its 2, but like a lot of people said, everything is two halfs, so if 1 plus half equals the full value, the half can only be one.
In the absense of compelling reasons to take a contrary view, questions like this should be read with the assumption that the question provides sufficient information with which to answer it. Therefore if you have a choice as to how to interpret the question, you should choose the interpretation which allows the question to be answered, rather than the interpretation which introduces an unknown. This is especially true when the first interpretation involves plain language reather than strictly technical definitions. I will go further and say that it is impossible to reason with people who do not follow this rule.
I disagree. The purpose of word problems like this is to exercise your problem solving skills. One important skill that you should have is determining whether you have enough information to get a reliable answer. Another is recognizing the assumptions that you make while analyzing a problem. Real life often gives you problems with out adequate information to solve them. It is good training to face similar situations where you have to admit ignorance or seek out more information before answering.
Sometimes in higher education, questions will be left vague because the instructor wants to see if you understand the concept well enough to recognize the missing variable/consideration. Or even that a listed variable is irrelevant.
If this problem were given as a short answer rather than multiple choice (which is also a reason to strongly consider the question was incomplete, since that's one of the few choices given), I would have probably written "assuming there are no taxes or fees on top of the listed price..."
I agree with you, Wanarunna. The two previous people who replied to you have never supervised a department of people and been held responsible for the work those people produce.
Once a supervisor's ass has been chewed out for his crew's bad work, he begins to be much more careful with how he words the assignments he gives to his subordinates. This problem would get a very serious rewording before it was assigned to a subordinate.
@@deezynar I have been a supervisor before. That's why I worded my response around education. This question would never be assigned to a subordinate because it doesn't make sense in a work setting to begin with...
@@isaac_marcus
Yes, the question as posed in the video is not clear enough to be used in most environments outside of mathematical education. We agree on that.
I tried to restate it to make it clearer, and I realized I couldn't come up with a better way of saying it. My inability bothers me more than the original question does, and that's not insignificant.
Yeah, I'm going to have to disagree with this one. I would have let it slide if the D choice wasn't available, but it was, meaning you should be interpreting the problem much more strictly, and in this case the meaning is ambiguous and that itself makes it not determinable. Appealing to the dictionary is a fallacy as it isn't the true authority, it is a attempt to codify language, but not infallible, hence why we have many dictionaries with different definitions. Appealing to the book also fails as they too can be wrong (you've had many incorrect solution given in this vary channel to other problems, so deferring to the answer key is not proper). I can definitely give that $2 is a potential solution, but not the ONLY solution, therefore it is not determinable.
As a non-english speaker, I did not get that "A book costs $1" as its production cost, but as "A book sells at $1". Therefore I got heavily confused by the question as I was reading:
"A book sells at $1 plus half its price. How much does it sells at".
I fell in the "The value cannot be determined". Even with the equation you provided, I was like: "nope I disagree", until I understood that not only "to cost" can refer to "the production cost", but it was actually the most common interpretation!
😅
I read it this way: A book costs "the price" plus half of "the price". The wording made me read it in this way. Only when I did this: "A book costs: $1 plus half its price.", I was able to understand what the author of this puzzle meant.
Sitting in a math classroom or in front of this RUclips video the answer may be $2, but in real life the answer would be “the value cannot be determined “ until you know what the seller priced the book at.
As in a half-price bookstore raising money for charity and adding $1 to their half-price price for the charity.
To some people, cost and price are two different concepts. Cost is how much money is spent to produce something. Price is what that something sells for. One could argue that this problem is unsolvable at best, and ambiguous at worst.
Mathematics is about rigour and unambiguity.
Therefore, if it’s a mathematics problem, we should not accept that price and cost can be used interchangeably.
Going from having 28% to 22% on the right answer is an evolution, but in the wrong way.
You should be rooting for rigour and unambiguity, not for the perpetuation of ambiguous wording of problems.
This is not an English test, it’s a maths test.
Buying this book is like falling into a math rabbit hole-$1 plus half its price, and then half of that, and half of that... it's the book that keeps on costing!
And if you keep on adding half till infinity you never get to the cash register!
sooo it costs a dollar plus 50 cents plus 25- hang on a minute, the book just costs 2 dollars again
@@adamrussell658 And yet, the cashier still takes your $2, hands you the receipt, and tells you to stop staring at the counter and let the person behind you make a purchase.
@@Moonlite_Kitsuneno. It costs
$1.50 in the first iteration
$1.50+$1.50/2 in the second
...
This already equals to $2.25
What I mean is that the price updates every time and the half of that gets added to the new price and so on.
This is a very common pattern found in (procedural) programming. So it's really not far fetched to think of the problem like this when you have a programming background.
Yup, easy peasy - I did it same way, except used I used p for price instead of b, and did it in my head.
And can also substitute the result/answer back into the original question, and see that it's clearly the correct answer.
Wow!
20 years Mind Your Decisions!
Taking the statement as originally worded, the correct equation is, as you say, b = 1 + b/2.
b = 1 + b/2 => b - b/2 = 1 => 2b/2 - b/2 = 1 => (2b - b)/2 = 1 => b/2 = 1 => b = 2
Apart from the reason given, where 'cost' is interpreted to mean 'cost of production', the only other way I can think of to reach the conclusion that the cost cannot be determined is to assume that the statement is incomplete, and expand it to read "A book NOW costs $1 plus half its ORIGINAL price", which would make the current cost impossible to determine.
On first though I was duh easy 1,5$. But when you wrote down the formula: b=1+b/2 it all made sense and ofc its 2$.
1.5 not 1,5
Speak English
@Emile.gorgonZola why are you so mad about a simple mistake like that 😭
Please ignore the commenter above and continue to use the decimal comma. I wish I was brave enough to stand up to the decimal point supremacists!
@@FlyingFox86Decimal comma on top
@@Emile.gorgonZolayou do realize in most of Europe they use , over .
Price and cost cannot be used interchangeably, however when someone buys something, the price he pays becomes his cost is he tries to sell it, hopefully at a price higher than the price he paid.
An argument for indeterminate is that price and cost are different things even when both are on the consumer side.
That is, the price may be $9.99, but we all know it is going to cost me $10.90, after tax.
So, the price is subtotal, and the cost is total.
Meaning the answer is cannot be determined, all we know is that there is some fee of $1 (and an apparent discount)
The question never talks about "the cost" (noun). It merely asks "how much does it cost?".
In economies where "price" doesn't include tax, the tax can be considered the cost of the transaction, not an amount that's included in what the book costs. Likewise, if you paid $3 postage to have the book sent to you by mail, or spent $3 in public transport tickets in order to get to the bookstore and buy this book, then those $3 are the cost of making the purchase, but generally (from the consumer side) it's not considered to be included in what the book costs.
(By the way, here in the Netherlands, from the consumer side, the tax is always included in the price.)
@@yurenchu this didn't respond to what I said nor make sense regarding American English usage of "cost". Maybe it's regional
@@JamesD2957 Well, your comment didn't respond to the video's question, because the video talks about "how much does the book cost?" (where "cost" is a verb) while you are talking about "the cost" (noun). The video's question never says "the cost".
Moreover, would you consider the price of a bus ticket in order to get to the bookstore as part of how much the book that you're buying costs? If no, then why would you do so with the tax?
The video's question is simply a concise question, and we may assume it's complete: every specific thing we need to know, may be presumed to be present in the question. If it doesn't mention, say, any bus ticket fares, we may assume that bus ticket fares are irrelevant to the question; so either the bus fare is not included in the price and also not in how much the book costs, or the bus fare is tacitly included in the price and hence also in how much the book costs. Either way, it doesn't change the fact that the correct answer to the posed question is simply $2 . And what applies to, say, bus ticket fares, also applies to other (apparently irrelevant, because non-specified) details such as tax.
@@yurenchu wow, that was a lot of words to say "I don't understand there are regional uses of words and I'm going to refuse to acknowledge that to pretend I'm right about something"
feel better
@@yurenchu bus tickets? lol
wow, feel better
It sounded like this was an infinite recursive result. $2 seems so weird so an answer. I still don’t get the solution, but I will yield to your expertise.
When you did you subtracted b/2 from both sides, how does b-b/2 = b/2. I don’t understand. Could you clarify so I understand?
Due to the warding, you can not assume weather the cost is refereed from the customer's (who buys the book from the store) perspective or the seller's (who sells the book in their store).
To the customer, it costs the book's price.
To the store, it costs as much as they pay to the factory.
Since it is translated from Russian, in English it becomes unclear, but reading in Russian you would more or less be certain that is it x = 1 + (1/2)x
Is pretty clear in English too. The last part of the question refers to the cost, as does the first. There's no confusion. I think the only reason people pause is because they expect it's a trick question, while it's not.
But the book itself says the answer is $2, so it's not a translation issue.
There’s another sense in which price differs from cost: tax. In the US, the price of an item rarely includes tax, so the cost paid by the purchaser can be significantly different than the price. (Also, there's a trend in charging fees that are only disclosed to purchasers at the moment of sale, so that's another way price can differ from cost.)
I learned it as a kid like this: a hare weighs 10 pounds plus half its weight. What is the hare's total weight?
No price vs costs issue.
Oh, I know this one. The hare is a butcher. He weighs MEAT.
It's not issue of people failing at math but rather an issue of communication I thought it was ment to be read as "A book cost $1. Plus half its value. Hiw much is the book?" From there the book is a dollar half a dollar is $0.50 there for its $1.50. It's like a really bad riddle
there is no ambiguity given there is no "." or "," after the $1. I think it was made as a puzzle to confuse people when not in the context of mathematics.
@@sashime00 So if a book's cost is $1 plus a tax of 50%, how much is the book, and how can I not read that based on what's literally written out?
* meant
I can see where you're coming from with the idea that the terms "price" and "cost" can be used interchangeably but that's just a matter of your being a math and economics guy rather than an english guy. "Price" and "cost," even in the context of being viewed from an entirely consumer perspective, do not have precisely the same meaning. The price of a thing is the value placed on its sticker on the shelf. How much it costs is the price plus any miscelaneous taxes or fees on the purchase. Outside the US, most purchases will have those as the same value but within the US and with quite a number of intangible products they simply aren't. 2 may be the intended answer and one that's easy to come to but it's an answer that relies on taking the written portion of the process much less precisely than the mathematics.
Price being a subset of cost, the answer is indeterminate without the price being given or at least information that can lead to it being given.
Given that the question is not originally in english though, we can mark that down as a translation error; someone trying to avoid redundance in the writing without considering the mathematical implications of changing the word used that way.
As a word problem, it’s not *fully* constrained (cost vs price), but assuming that they are used interchangeably, before sales tax or VAT, $2
I suspect that many, if not all, of the people who answered $1.50 or $1 were using what Daniel Kahneman called "System 1" or "fast" thinking (in his book Thinking, Fast and Slow).
I understood it this way: The price is $1. But wait, there is more: a half of that price more. Therefore I thought it either should be $1.50 or it can't be solved because the price can't be $1 and $1.50 at the same time. After the solution was given, I added ":" after "costs" and then it made more sense to me: "A book costs: $1 plus half its price."
Cost is the money needed to produce the book. Price is what it sells for. Therefore b= 1 +b/2 is nonsensical as it requires cost and price to be the same thing. The equation is c= 1+p/2. This cannot be determined as p is unknown. If the price of the book is 5, then the cost of the book is 3.5. Don't try to make calculations based on misuse of language.
It takes until 1:10 to explain the correct solution. What is the rest of the video for?
If you have to resort to a dictionary and parsing the language of the question, you're probably going about it wrong.
If A=B+A and B=A+C, then which variables can have their values determined, if any.
Please make a video on this.
a: -1/1
B: 0
C: opposite of A
in fact, that works with literally any number
@@Safetyswitch Replace the ones in a's value with variables and you are 100% correct!😀
I don't think there is much of a video to be made about that. B=0 and A=-C
Unless I'm missing something.
A-A=B+A-A` B=0` A+C=0` A=-C` C=-A
Books are often discounted from the cover price, so I fall into the price does not equal cost group
I thought it was $1.50 because the book cost is $1 + half its price (0.50), but see I'm wrong.
If its prices is 1 its prices isnt 1.5 because 1 is Not 1.5
I got the same answer as you, $1 + 50% = $1.50
it costs $2 because 1+x=y with x=0.5 y and y beeing the price whole price (=1+ price/2). so y-1=0.5 y --> 0.5 y = x = 1
@@marks.9448but we assumed that $1 was it's base price and you have to pay an additional 50% of it's base price. Imagine it like you have a tax rate of 50%
@@zekiz774 if its price was $1 it would cost $1 and not $1 + 0.5 $1. and in civilised countries taxes are included in prices
Some people 'over-think' the problem...but isn't that what the problem is designed to do? The FAA Practical exam for A&P Mechanics has a question this reminds me of: A blimp is flying at one mile altitude on a cloudless day at the equator. It casts a clear shadow on the ground. Is that shadow: a. larger than b.smaller than or c. the same size as the blimp?
The 'correct' answer was c. the same size....but I picked a. larger than because the 'rule of shadows' says that any shadow MUST be larger than the object that created it. The explanation given when I challenged the answer was that being the sun is 93 million miles from earth and the blimp only one mile in altitude, for all intents and purposes the shadow will be the same size. I argued that the question didn't say 'for all intents and purposes' which obviously would have made 'same size' the right answer being the difference in size would be microscopically small..but TECHNICALLY (and aren't we trying to train everyone to be a detail oriented technician here?) a shadow MUST be larger so this is an invalid question. They relented and gave me credit for the answer in the end.
When a question that the originators think has a clear answer and someone gets it 'wrong'....in fairness the person should be given the chance to explain WHY they came up with the 'wrong' answer and many times their thinking will actually be a lot deeper and more technically correct than what the question was looking to find and they should be credited properly for it.
I think it would be interesting if the question was rephrased to change the word price to cost. Would this significantly alter the results you obtained, I wonder?
The question can't be answered. The item is not being sold for it's full value if its costs 1 dollar and half of it's price. We don't know that the initial price was, and therefore we can't answer the question. The book could have an initial cost anywhere from $1 to $100. It doesn't specify what the initial price is, and the initial price is not 1.
This question is written to be confusing on purpose.
If the “plus half its cost” is considered a tax of 50%, the total price is $1.50. The book costs $1 plus tax, the tax is 50%. You would never calculate the 50% after adding the 50%.
If the tax is 50%, the base price is the same as the tax, therefore price cannot be 1.50
The word 'cost' is relative - it is the amount of money that the purchaser must part with. The important thing is, who is the purchaser? Cost == price for an end consumer (obviously the subject of this question), compared to manufacturing cost to a manufacturer.
The number of respondents is also significantly down. I wonder if the shifting response proportions could be explained better by a change in who still answers surveys on twitter(? Fb?), the increasing average age of people on the social media platform in question, or some other factor?
price = 1
while True:
price += price / 2
For some reason that was my initial thought. Inflation has fucked me up
There is a legitimate reason to believe differently. Cost can also mean the total cost to the customer. For those of us who have to pay taxes or other such charges that is higher than the listed price. The total cost of a $10 book with a 10% sales tax would be $11 even though the listed price of the book is only $10. As we do not know the reason for the said extra charge of $1 stated in the problem; it could simply be a $1 surcharge on all purchases, we cannot know the price of the book in that scenario. As this is a math puzzle that solution doesn't make as much sense, but if this were a more general puzzle of trying to figure out what the information given to us means, then D would certainly be a correct answer.
I still can't believe in the US the listed price on an item isn't what you pay in stores... It feels like a scam. It's not like that in the EU/UK tax has to be included on the listed price of the item.
This hinges heavily on the definitions of price and cost, and leads me to D if I want to get all clever about it. If I want to just do the math problem, then it's B, because 1 plus half of 1 again is 1.5. If you want to go way harder than necessary on the math, then it's C. You have to do even weirder stuff to get A somehow.
Every time I see a math problem that gets a lot of popularity on the internet, I know it has to be one that has varying answers based on operations or context.
Didn't we already do this one? Oh yeah, the poll you mention at 1:20.
Think of price/cost in this problem like this: the _price_ is what the seller charges and the _cost_ is what the customer pays. A cost is always what someone pays for something, so from the customer's perspective the expenditure is a cost. Seeing it like that, a price is _never_ a cost because it might differ from what the customer ends up paying.
There's probably a better way to describe that in econ-speak but that's how I understand it.
P.S. Also, when someone sells something, nobody asks them "What cost did you get for it?" It's always "What price did you get for it?!
But the question never uses "cost" as a noun, only as a verb.
Elementary algebra 1 + x/2 = x, we get x = 2
One thing it does highlight is that having come to an answer, a lot of people don't work it backwards to check it's correct - which seems to me to be a very obvious thing to do.
I don't disagree with you that people who are contrasting price vs. cost are overthinking. That said, it would be useful to try a poll about the question at some point in the future where you word it as either:
A. The price of a book is $1 plus half of its price. What is the price of the book?
B. A book costs $1 plus half of its cost. What is the cost of the book?
If very few people said it could not be answered, that would be evidence to support your hypothesis that people are being nit picky about price vs. cost.
hello from greece. a version of this question was in the math book we had in school when i was 7-8 years old. third grade if i remember correctly. our version was .. a brick weigh is 1 kilo and half a brick how much does the brick weigh? (sorry for my english)..
It depends on how the book is priced relative to its cost. So the answer is D. The missing info here is what is the price of the book.
I think the problem with so many people getting $1.5 is because its money, we immediately think “it was $1, but the store had to increased the price by 50%” which then comes out to $1.50, correct?
I think because it’s money I automatically changed the wording for it in my head.
I kept getting $1.5 when thinking about it myself until I saw someone who changed it to “a brick weighs 1 pound…” and then it made sense
It's a matter of people not understanding how to think, speak or read properly.
Please launch course on how u create video in detail. I mean in detail which softwares u use and I'm interested in starting RUclips channel and create videos in my domain. I would love to join the course if u launch it and plz let me know if u got any such kind of thought in your mind.
Here's a real example:
Ignoring taxes, "something" costs $37 plus half its price. How much does "something" cost?
Going by the premise of the book, the supposed cost of this "something" is supposed to be $74 dollars.
Hint: it's not.
Additional hint: think Las Vegas.
Final hint: Think resort fees and a 50% discount off the room rate (listed as the price of the room by a famous booking site).
The cost/price for the room before taxes, is $61.
$24 is half the price of the room ($48 is full price), $37 is a resort fee, both are subject to a 13.38% tax.
Has nothing to do with cost v. price as presented in the video. The above example is from a consumers point of view. Nothing to do with overthinking the problem.
It's a poorly written problem that ignores how commerce works. The answer should be not enough information.
I think many are thrown off thinking that they need to decipher the semantics of the question. Overthinking is your downfall here. Plus, since the price was denoted in unspecified “dollars”, and unless one knows the origin of the riddle, one could easily jump to the conclusion that it may be from the US and start thinking about “are we adding tax here or something?”
I guess the one thing that could improve the question for clarity would be to not use both the terms ‘cost’ _and_ ‘price’ in the same question. But then again, wouldn’t that take some of the fun away?
I see the question, I see his algebra, I see that his algebra is logical, but I don't see the question leading to that algebra.
Any supervisor who asked that question of a subordinate and was responsible for a correct answer, has less than a 2/3 chance that the answer he gets will be correct. There must be a way to state the question so the correct answer can be assured.
I found myself initially thinking of the problem as being 1 + the infinite series 1/2 + 1/4 + 1/8 + ... + 1/2n, which also ends up being 2. b = 1 + b/2 is definitely better though
Mind Blowing ! I went wrong by letting 'x' be the value of the book.
After that, the equation expanded and accidentally invented Time Travel, taking me back to 1955.
Some hairy dude showed me the equations for Clean Energy, Cure for Cancer, Space Travel etc.
Unfortunately (as a joke) i asked him if the answer was 2, so he angrily erased 'x' and wrote 'y', which instantly put me back here in 2029, where i started.
The Value of all that really cannot be determined.
How much DOES it COST? "Cost" is also a verb here, so the whole discussion whether it means price (noun) or cost (noun) is pointless. If the wording were:"What is its cost?" then that argument would be valid. But it is crystal clear. I'm disappointed at Presh, that he didn't notice that "costs" and "does... cost" both are verbs. Even I, as a non-native speaker of English, picked up on that.