Question

Frank is 3 times as old as Ken. Frank is also 15 years older than Eileen, while Ken is 1 year younger than Eileen. What are the ages of Frank, Eileen, and Ken? Use an algebraic equation and define your variables.

Answer 1

Ken is 8, Frank is 24 and Eileen is 9.

Let k = Ken's age.

We know that Frank is 3 times as old as Ken, so Frank = 3k.

We know that Ken is 1 year younger than Eileen.  This means that Eileen is 1 year older than Ken, and Eileen = k+1.

Frank is 15 years older than Eileen, so Frank is (k+1)+15.

This gives us two expressions for Frank; we can set them equal to form an equation to solve:
3k = (k+1)+15

Combine like terms on the right:
3k = k+16

Subtract k from both sides:
3k-k = k+16-k
2k = 16

Divide both sides by 2:
2k/2 = 16/2
k=8

Ken is 8.
Frank is 3*8 = 24.
Eileen is 8+1 = 9.