Joe is twice as old as Tom. Six years ago, joe was three times as old as Tom was then. What is joes current age?

Question

If possible please show steps to answer.

Answer 1

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

Answer 2

Let j = Joe's current age, and t = tom's. Translating the words into equations:

j = 2t

j - 6 = 3(t - 6) ---> j - 6 = 3t - 18, and j = 3t - 12. Setting the 2 equations for j = to each other gives

2t = 3t - 12, so t = 12.

(It follows that j = 2t = 24, and you can verify the solution by plugging back into the original equations)