Mike S. answered • 01/17/20

SAT/ACT & Math Tutor- Recent Notre Dame Grad

First, we want to translate this problem into algebraic equations

Define the variables

J = Joe's Age

T = Tom's Age

From the first sentence, we see that Joe's age is twice Tom's age. We write that as the following:

**J = 2T**

From the second sentence, we see that 6 years ago, Joe's age was 3 times Tom's age. Before multiplying Tom's age by 3, we would subtract 6 from both T and J. Then, we write that as the following and simplify:

J - 6 = 3*(T - 6) Distribute 3 to the T and -6

J - 6 = 3T - 18 Combine like terms

**J + 12 = 3T**

Now that we have a system of equations, we can substitute our value for J in the first equation, into the second equation:

(2T) + 12 = 3T

Subtract 2T from both sides:

12 = T

Plug this value into one of the prior equations:

J = 2*12

J = 24