Question 1207224
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Answer: <font color=red>12</font> 


Explanation


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 = <font color=red>12</font> 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.
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