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.

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.