The sum of the ages of Brendan and Ashton is 84 years. 10 years ago, Brendan's age was 3 times Ashton's age. How old is Brendan now?

Question

The sum of the ages of Brendan and Ashton is 84 years. 10 years ago, Brendan's age was 3 times Ashton's age. How old is Brendan now?

Answer 1

Hello Nadine,

 

Let's assign some variable first

B = Brendan's age today

A = Ashton's age today

 

B-10 = Brendan's age 10 years ago

A-10 = Ashton's age 10 years ago

 

From the first sentence, we know

1) B + A = 8

or

84-B = A

 

From the 2nd sentence

2) B-10 = 3(A-10)

 

Let's use substitution and substitute 84-B = A for A in equation 2).

This gives us.

B-10 = 3(84-B-10)

B-10 = 3(74-B)

B-10 = 222 - 3B

4B = 232

B = 58