Question

Susan is 3 times as old as Paul and Paul is 3/2 times as old as Mary. What fraction of Susan's age is Mary?

a) 3/8 b) 2/9 c) 15/4 d) 6 e) 13/2

Answer 1

b) 2/9.

Explanation:

Let Mary's age be x , then:

Paul's age is (3/2)x.

Susan's age = 3(3/2)x = 9/2 x.

So Mary is 2/9 the age of Susan.

Answer 2

2/9

Explanation:

We are given Susan (S) is 3 times as old as Paul (P) so S=3P.

And Paul (P) is 3/2 times as old as Mary (M) so P=(3/2)M.

What fraction of Susan's age is Mary?

So if S=3P and P=(3/2)M, then by substitution we have

`S=3((3)/(2))M`

`S=(9)/(2)M`

Multiply both sides by the reciprocal of 9/2 resulting in:

`(2)/(9)S=M`

This says Mary is two-ninths the age of Susan.