Five years ago, Tim is twice as old as Joshua. But currently, Joshua is just ten years younger than Tim. How old is Tim three years ago?

Answer 1

Let :

T = Tim's age today

J = Joshua's age today

Thus : (T-5) & (J-5) represent how old they were 5 years ago

We need to setup equations based on the information we are given :

First Equation :

(T-5) = 2 * (J-5)

(T-5) = 2*J - 10

T = 2J - 5

Second Equation :

T = J + 10

Since we have 2 unknown variables and 2 equations, we can solve by plugging one into the other. See below :

Let's solve for 'J' first

T = 2J - 5

J + 10 = 2J - 5

10 = J - 5

15 = J

Solve for 'T' next (you could of went straight and solved for T, but I like to solve for all variables in a problem.)

T = J + 10

T = 15 + 10

T = 25

3 years ago, Tim would be :

T_{3 years ago} = T-3 = 25 - 3

T_{3 years ago} = 22

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Always check your work!

5 years ago, Joshua would of been 10 and Tim 20, which is correct since the statement says Tim was twice as old as Joshua.

Currently, Joshua is 15 and Tim is 25, which is correct since the statement says Tim is 10 years older now.

Correct!