Question 1191544
<br>
Technically, the problem as stated has no solution in whole numbers and is therefore invalid.<br>
The problem is that a phrase like "2 times older than" should NEVER be used in the statement of a problem, because its meaning is NOT what most people think it is.<br>
Given an age n, the age "2 times AS OLD AS" n is clearly 2*n = 2n.  That is clearly what the intent of this problem is.<br>
But if an age n is given, and another age is "2 times OLDER THAN" n, then the grammatically correct interpretation is that the other age is n, PLUS 2 TIMES MORE n, which is n+2n=3n.<br>
(Note that corresponds to saying that a number INCREASED BY 200%, becomes 100%+200% = 300% of the original number.)<br>
So "2 times older than" means "3 times as old as".<br>
Then the correct interpretation of the problem as written is
x = John's age
x-2 = Jill's age
3x+8 = Tom's age<br>
And the equation that says the sum of their ages is 82 leads to non-integer values:<br>
x+(x-2)+(3x+8)=82
5x+6=82
5x=76
x=15.2<br>