Question 1207224: Tommy’s age is 2/3 Ben’s age now. In 8 years time, the ratio of Tommy’s age to Ben’s age will be 10:13. How old is Tommy now? Found 3 solutions by math_tutor2020, mananth, josgarithmetic:Answer by math_tutor2020(3816) (Show Source):
The ratio of their future ages, Tommy to Ben, is 10:13
That scales to 10x:13x for some positive integer x.
Subtract 8 from each to get their present day age.
Tommy = 10x-8
Ben = 13x-8
We're told that Tommy's current age is 2/3 of Ben's current age.
So,
Tommy = (2/3)*( Ben )
10x-8 = (2/3)*( 13x-8 )
3(10x-8) = 2(13x-8)
30x-24 = 26x-16
30x-26x = -16+24
4x = 8
x = 8/4
x = 2
Then compute 10x-8.
10x-8 = 10*2-8 = 20-8 = 12 is the answer.
Check:
Ben would be currently 18 since 13x-8 = 13*2-8 = 26-8 = 18
Note that 12 is 2/3 that of 18, which helps partially confirm the answer.
In other words, 12/18 = 2/3.
Add 8 to each present day age to find that Tommy and Ben will be 12+8 = 20 and 18+8 = 26 respectively.
The ratio 20:26 reduces to 10:13 when dividing both parts by the GCF 2.
The answer is fully confirmed.
You can put this solution on YOUR website! Tommy’s age is 2/3 Ben’s age now. In 8 years time, the ratio of Tommy’s age to Ben’s age will be 10:13. How old is Tommy now?
Let Ben's age be x
Tom'my's age will be 2x/3
In 8 years
Ben's age x+8
Tommy's age will be (2x/3 )+8
the ratio of Tommy’s age to Ben’s age will be 10:13.
(
(2x/3)+8) /( x+8) = 10/13
((2x+24)/3 )/(x+8)= 10/13
(2x+24)/3(x+8) =10/13
(2x+24)/(3x+24) = 10/13
13(2x+24)= 10(3x+24)
26x +312 = 30x +240
4x = 72
x = 18 Ben's age
Tommy's age = 2/3 * 18 = 12 years now
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