Question 1202434
<br>
Note that you have received two earlier responses, one showing a single solution and another showing two solutions.<br>
If we want to be mathematically correct, there is only the one solution.  The second solution is possible only if we don't follow strict mathematical rules.<br>
In everyday English usage, the difference between 5 and 3 is 2, and the difference between 3 and 5 is 2.  The order is not important; the difference is always considered to be positive (or non-negative).<br>
However, in mathematics, the order is important.  The difference between a and b is always a-b; it is never b-a.  So in mathematics the difference between 5 and 3 is 2, but the difference between 3 and 5 is -2.<br>
So in your problem, if x is Tim's age and y is Tala's age, then the difference between twice Tala's age and Tim's age is 2y-x.  That leads to the single mathematically correct solution to the problem:<br>
x + y = 36
2y - x = 12
3y = 48
y = 16
x = 36-16 = 20<br>
ANSWER: Tim 20, Tala 16<br>
With that solution, the difference between twice Tala's age and Tim's age is 12, as it needs to be: 2(16)-20 = 32-20 = 12.<br>
To get the second, mathematically incorrect, answer, we need to have the difference between twice Tala's age and Tim's age in the wrong order:<br>
x + y = 36
x - 2y = 12
3y = 24
y = 8
x = 36-8 = 28<br>
mathematically incorrect answer: Tim 28, Tala 8<br>
With this incorrect solution, the difference between twice Tala's age and Tim's age is NOT 12: 2(8)-28 = 16-28 = -12.<br>