The sum of Tess, Audrey, and sams age is 38. Tess is 2 years older than audrey, and Sam is 29 years younger than three times audreys age. What are each of there ages

Answer 1

You can set it up as follows:

Tess (T) + Audrey (A) + Sam (S) = 38

T = A + 2

S = 3A - 29

You need to be able to solve for one variable at a time. As we can already see everything expressed in terms of A, let's start there. We will plug in for T and S in terms of A to our original equation.

(A + 2) + A + (3A - 29) = 38, which simplifies to:

5A - 27 = 38

5A = 65

A = 13

Now we know Audrey is 13 years old. To get the remaining ages, go back to our secondary equations, and plug in A.

T = A + 2, or T = 13 + 2; T = 15

So Tess is 15 years old.

Now we have two different equations to choose from to get the remaining age, Sam's. Let's use the easiest equation, T + A + S = 38.

So, 15 + 13 + S = 38

This tells us S = 10

So, we know Sam is 10 years old, Audrey is 13 years old, and Tess is 15 years old.

Hope that helps!!

-Jack Epner