Algebra Word Problem

Question

Today, Jacob is 4 years older than Anthony. Nine years ago Christopher was 3 times as old as Anthony. If the total of the boys' ages is 66, how old will Jacob and Anthony be at Christopher's 30th birthday party?

Answer 1

Take is one small step at a time.

Let their current ages be J, A and C.

 

The first statement is easy. "Jacob is 4 years older than Anthony":

J = A+4

 

"Nine years ago..."

Christopher was (C-9) and Anthony was (A-9)

"Christopher was 3 times as old as Anthony."

(C-9) = 3(A-9)

C-9 = 3A-27

3A-C=18

 

"the total of the ages is 66"

A+C+J = 66

Substitute (A+4) for J

2A+4+C = 66

2A+C = 62

 

Add the second equation:

2A+C = 62

3A- C =18

5A = 80

A=16

 

J = 16+4

J = 20

 

A+C+J = 66

16+C+20 = 66

C = 30

 

Since Christopher is 30, his 30th birthday must be today!