Question

Currently, Sam's coach is three times older than Sam. When Sam started soccer 5 years ago, his coach was five times his age. How old is Sam now?

Answer 1

let sam=x
let the coach= 3x
x-5=3x(5)
solve from there

Answer 2

Sam's current age = S
Coach's current age = C

C = 3S [Sam's coach is three times older than Sam]
5(S-5) + 5 = C

So you have a system of equations.

C = 3S
C = 5(S - 5) + 5

Solve for any variable of your choosing. I'm going to solve for S because I think it's easier.

[C = 3S]
[3S] = 5(S - 5) + 5
3S = 5S - 25 + 5
3S = 5S - 20
-2S = -20
S = 10

We've found that Sam's current age is 10 years old. Given that the coach is currently three times Sam's current age, the rest of this problem is very easy.

3S = C
3(10) = C
C = 30

We've found that Sam's coach's current age if 30 years old.

It's always important to cross-check these results to see if the results are accurate. Use the other equation in the system of equations to verify.

C = 5(S - 5) + 5
30 = 5(10 - 5) + 5
30 = 5(5) + 5
30 = 25 + 5
30 = 30

The answers we've gathered are accurate. Sam's current age is 10 years old while his coach's current age is 30 years old.