Question 1209951: Hi
When tara was 3 years old Joe was 1/3 of Tara's current age. When Joe was 13 years old Tara was 1/3 of his current age. How old are each of them now.
Found 3 solutions by Edwin McCravy, greenestamps, josgarithmetic:
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
Sorry, your '13' is a typo. I think you accidentally interchanged the digits and
meant to type '31' instead of '13'.
So I will do this problem instead, with '13' changed to '31'.
When Tara was 3 years old Joe was 1/3 of Tara's current age. When Joe was 31 years old
Tara was 1/3 of his current age. How old are each of them now?
T = Tara's present age
J = Joe's present age
When Tara was 3 years old, Joe was...
Let that be x years ago, so T-x=3, and Joe was J-x
...Joe was 1/3 of Tara's current age.
When Joe was 31 years old Tara was...
Let that be y years ago. Joe was J-y=31 and Tara was T-y
...Tara was 1/3 of his current age.
How old are each of them now?
 ,
Solve that by hand, or put it in any system solver. There are a number
of them online.
Get J=57, T=45, x=42, y=26
Let's check:
When Tara was 3 years old,...
Tara is 45, so x=42 years ago she was 45-42 = 3.
That checks.
Joe was 1/3 of Tara's current age.
Joe is 57, so y=26 years ago, he was 57-26 = 31
So that checks.
When Joe was 31 years old Tara was 1/3 of his (Joe's) current age.
y=26 years ago was when Joe was 31, and Tara was 45-26=19. And sure enough,
19 is 1/3 of 57, which is Joe's present age.
Answer: Tara is 45 and Joe is 57.
Edwin
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
I read the problem differently than the other tutor....
"When Joe was 13 years old Tara was 1/3 of his current age." I read that to mean Tara's age when Joe was 13 years old is one-third of TARA'S age now.
Starting with that....
Let x = Tara's age when Joe was 13
Then 3x = Tara's age now
Tara Joe
------------
3x ?? their ages now
x 13 their ages when Joe was 13
When Tara was 3 years old, Joe was 1/3 of Tara's current age.
Tara Joe
------------
3x ?? their ages now
x 13 their ages when Joe was 13
3 x their ages when Tara was 3
The difference between their ages is constant:
13-x = x-3
16 = 2x
x = 8
Tara Joe
------------
24 ?? their ages now
8 13 their ages when Joe was 13
3 8 their ages when Tara was 3
Joe is 5 years older than Tara, so...
Tara Joe
------------
24 29 their ages now
8 13 their ages when Joe was 13
3 8 their ages when Tara was 3
ANSWERS: Tara is now 24; Joe is 29
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Note on proper English....
"How old are they now?"
or
"How old is each of them now?"
but not
"How old are each of them now?"
Answer by josgarithmetic(39625)  (Show Source):
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