EZ1. X represents sis, (X-10)+1 = (X-10)+1 +(X+10)+1 / 2 . 2(X-10)+1 = X-9+X+11 . In short 2X=20 X=10 Sam is 19 now sis is 9 next year Sam is 20 sis is 10
Alright, word problem algebra, very good. Let’s dig in. Here is the relevant info in bulletpoint form: -1.) Sam is 10 years older than his sister now -2.) In one year, Sam will be twice as old as his sister. -3.) We need to determine, if possible, Sam’s age now. Let’s start making equations. From point 1: s = t + 10, where s is Sam’s age now and t is his sister’s age now. From point 2: s + 1 = 2 * (t + 1) = 2t + 2 Solve this for s: s = 2t + 2 - 1 = 2t + 1 Notice we have two equations for the value of s. Set them equal to each other: t + 10 = s = 2t + 1 And now solve for t (remember this is not going to be our final answer): t + 10 = 2t + 1 2t - t = 10 - 1 t = 9 Plug this into our first equation: s = t + 10 s = 9 + 10 s = 19 And there is point 3 resolved: Right now, Sam is 19 years old.
gotta translate words to equations Variables: A: Sam's Age B: Sister's Age Equations: Eq.1: A = B + 10 Eq.2: A + 1 = 2×(B+1) A + 1 = 2B + 2 A = 2B + 1 Set Eq.1 = Eq.2 B+10 = 2B+1 9 = B use Eq.1 to find A Eq.1: A = B + 10 A = 9 + 10 = 19 VERIFY by Eq.2 Eq.2: A = 2B + 1 19 =? 2(9) + 1? 19 =❤ 19✔️
Since we were asked for Sam's age (today), why not allow the variable "X" to be Sam's age, rather than Sam's sister's age? A final math step can be avoided!
I could have come with an equation and solved for the age(s), but I solved it in my head too quick. I took math in the 1960’s. My grandparents would have been in the early 1900’s.
This is not an algebra word problem. This is a 2 times table problem. If Sam is 10 years older than his sister now then he will still be 10 years older than his sister next year. That's how time works. Next year Sam's age is 2×10 = 20 so currently Sam is 19.
Answer: 19 years. ----- Let the age of Sam be Y years. Let the age of Sam’s sister be X years. Sam is 10 years older than his sister means, Y = X + 10 --(1) Next year, Sam will be Y+1 years old and Sam’s sister will be X+1 years old. Next year, Sam will be twice as old as his sister means, Y+1= 2(X+1)--(2) Y= 2X+2-1 Y=2X+1 Substituting the above with equation (1), X+10= 2X+1 2X + 1 = X + 10 X = 9 Sam’s sister’s age is 9 years. Since Sam is 10 years older than his sister, Sam’s age= 9+10=19 years.
Sister = x Sam = x + 10 next year --> sister = x + 1 next year --> Sam = x + 10 + 1 = x + 11 x + 11 = 2(x + 1) x + 11 = 2x + 2 11 - 2 = 2x - x 9 = x Sam x + 10 = 9 + 10 = 19 years at the moment ✅ Sister = x --> 9 years at the moment next year Sam will be 19 + 1 = 20 years Sister will be 9 + 1 = 10 years
I understand that this is a math channel and I applaud those who created a formula. But the answer is so simple long calculations are overkill. Common sense and logic are much faster here. With any two siblings the older will only be twice the younger's age once. With a 10 year difference the ages have to be 10 and 20 years of age. In this example that doesn't happen for one year so the elder sib is 19.
@@ORRadtechExactly. Often this form of question constructed a bit differently, e.g. Currently Sam is three times as old as his sister and in 5 years time he will be twice as old. That might require a little bit of algebra, but the way he's written this means it's not an algebra problem at all.
Greetings. Happy Sunday evening to everyone. Blessings. Currently Sam is 19 and his beloved sister is 9 years old. Now for the calculations. Let us assume that Sam's sister is X years old. Based on this assumption, Sam would be X+10 years old. Further, one year later the sister would become X+1 years old and Sam would become (X+10+1) years old. Now, we were also told that subsequent to their initial ages of X, and X+10, one year later, next year, when brother and sister would have become X+11 and X+1 years old, the brother, Sam's age would be twice the sister's age. That is X+11=2(X+1), X+11=2X+2, 2X-X=11-2, X=9. Therefore, Sam's sister is currently, as we speak, 9 years old, the value of X we initially assumed to be her age. Sam's age is (X+10), (9+10)=19 years old.
EZ1. X represents sis, (X-10)+1 = (X-10)+1 +(X+10)+1 / 2 . 2(X-10)+1 = X-9+X+11 . In short 2X=20 X=10 Sam is 19 now sis is 9 next year Sam is 20 sis is 10
Alright, word problem algebra, very good. Let’s dig in.
Here is the relevant info in bulletpoint form:
-1.) Sam is 10 years older than his sister now
-2.) In one year, Sam will be twice as old as his sister.
-3.) We need to determine, if possible, Sam’s age now.
Let’s start making equations. From point 1:
s = t + 10, where s is Sam’s age now and t is his sister’s age now.
From point 2:
s + 1 = 2 * (t + 1) = 2t + 2
Solve this for s:
s = 2t + 2 - 1 = 2t + 1
Notice we have two equations for the value of s. Set them equal to each other:
t + 10 = s = 2t + 1
And now solve for t (remember this is not going to be our final answer):
t + 10 = 2t + 1
2t - t = 10 - 1
t = 9
Plug this into our first equation:
s = t + 10
s = 9 + 10
s = 19
And there is point 3 resolved: Right now, Sam is 19 years old.
You over-complicated it. The equation from point 2 is
s + 1 = 2 × 10
which very rapidly gives you s = 19.
gotta translate words to equations
Variables:
A: Sam's Age
B: Sister's Age
Equations:
Eq.1: A = B + 10
Eq.2: A + 1 = 2×(B+1)
A + 1 = 2B + 2
A = 2B + 1
Set Eq.1 = Eq.2
B+10 = 2B+1
9 = B
use Eq.1 to find A
Eq.1: A = B + 10
A = 9 + 10
= 19
VERIFY by Eq.2
Eq.2: A = 2B + 1
19 =? 2(9) + 1?
19 =❤ 19✔️
Same way I solved it but I used the letters b and s, for brother and sister.
I was going to use s for Sam but then sister started with an s
This took me all of 1 second to solve this.
19 years old now. His Sister is 9 Therefore next year his sister will be 10 and he will be 20
19
Since we were asked for Sam's age (today), why not allow the variable "X" to be Sam's age, rather than Sam's sister's age? A final math step can be avoided!
Yes. However some people might start out trying to work with the sister’s age as X and forget the final step. His way highlights that potential issue.
I could have come with an equation and solved for the age(s), but I solved it in my head too quick. I took math in the 1960’s. My grandparents would have been in the early 1900’s.
Same way I solved it but I used the variables B and s for brother and sister.
This is not an algebra word problem. This is a 2 times table problem.
If Sam is 10 years older than his sister now then he will still be 10 years older than his sister next year. That's how time works.
Next year Sam's age is 2×10 = 20 so currently Sam is 19.
great explaination thanks.
Sam is 19 his sister is 9
Answer: 19 years.
-----
Let the age of Sam be Y years.
Let the age of Sam’s sister be X years.
Sam is 10 years older than his sister means,
Y = X + 10 --(1)
Next year, Sam will be Y+1 years old and Sam’s sister will be X+1
years old.
Next year, Sam will be twice as old as his sister means,
Y+1= 2(X+1)--(2)
Y= 2X+2-1
Y=2X+1
Substituting the above with equation (1),
X+10= 2X+1
2X + 1 = X + 10
X = 9
Sam’s sister’s age is 9 years.
Since Sam is 10 years older than his sister, Sam’s age= 9+10=19 years.
Sister = x
Sam = x + 10
next year --> sister = x + 1
next year --> Sam = x + 10 + 1 = x + 11
x + 11 = 2(x + 1)
x + 11 = 2x + 2
11 - 2 = 2x - x
9 = x
Sam x + 10 = 9 + 10 = 19 years at the moment ✅
Sister = x --> 9 years at the moment
next year Sam will be 19 + 1 = 20 years
Sister will be 9 + 1 = 10 years
19 yrs
Next year OR one year from today?
19 without resorting to linear equations...
Sis = S and Bro = B so B = S + 10 and B + 1 = 2 x (S + 1)
(S + 10) + 1 = 2S + 2 -> S = 11 - 2 = 9 yo
B = 19 yo
That is the way I did it.
now sam is 19 yr.ans(sister now 9yr)
It took me maybe 5 seconds to solve it in my head.
Congrats.
I had no idea how to account for the additional year.
I understand that this is a math channel and I applaud those who created a formula. But the answer is so simple long calculations are overkill. Common sense and logic are much faster here. With any two siblings the older will only be twice the younger's age once. With a 10 year difference the ages have to be 10 and 20 years of age. In this example that doesn't happen for one year so the elder sib is 19.
@@ORRadtechExactly. Often this form of question constructed a bit differently, e.g. Currently Sam is three times as old as his sister and in 5 years time he will be twice as old. That might require a little bit of algebra, but the way he's written this means it's not an algebra problem at all.
@@gavindeane3670
Sam = 3Sister
Sam + 5 = 2(Sister + 5)
SUBSTITUTION:
3Sister + 5 = 2(Sister + 5)
3Sister + 5 = 2Sister + 10
3Sister - 2Sister = 10 - 5
Sister = 5
SINCE:
SAM = 3SISTER
SAM = 3(5)
SAM = 15
19
Sam is 19
He's 19 yo now.
Obviously 19.
19.
Sam = Sister + 10
Sam + 1 = 2(Sister + 1)
SUBSTITUTION:
Sister + 10 + 1 = 2(Sister + 1)
Sister + 11 = 2(Sister + 1)
Sister + 11 = 2Sister + 2
11 - 2 = 2Sister - Sister
9 = Sister
SINCE:
SAM = SISTER + 10
SAM = 9 + 10
SAM = 19.
@round2 you are the best math teacher.
@@josiahndungu4269 You are the best math student.
Greetings. Happy Sunday evening to everyone. Blessings. Currently Sam is 19 and his beloved sister is 9 years old.
Now for the calculations. Let us assume that Sam's sister is X years old. Based on this assumption, Sam would be X+10 years old. Further, one year later the sister would become X+1 years old and Sam would become (X+10+1) years old. Now, we were also told that subsequent to their initial ages of X, and X+10, one year later, next year, when brother and sister would have become
X+11 and X+1 years old, the brother, Sam's age would be twice the sister's age. That is X+11=2(X+1),
X+11=2X+2,
2X-X=11-2,
X=9. Therefore, Sam's sister is currently, as we speak, 9 years old, the value of X we initially assumed to be her age. Sam's age is (X+10),
(9+10)=19 years old.
19
19
19