Can somebody help me with this?

Question

If the ratio of the ages of two friends A and B is in the ratio 3 : 5 and that of B and C is 3 : 5 and the sum of their ages is 147, then how old is B?

1. 15 years

2. 75 years

3. 49 years

4. 45 years

5. 27 years

The answer is 45 years, but what is the correct approach to solve it?

## Know the answer but need an explaination

### Re: Know the answer but need an explaination

A/B = 3/5

B/C = 3/5

A + B + C = 147.

Expressing from first two A = (3/5)*B and C = (5/3)*B, putting them into last one and multiplying all by 15 gives

9B + 15B + 25B = 147*15

49B = 2205

B = 45.

Btw., this forum is for mathematicians preparing for the GRE Subject Test, which is different from Quantitative Section of the GRE General test.

B/C = 3/5

A + B + C = 147.

Expressing from first two A = (3/5)*B and C = (5/3)*B, putting them into last one and multiplying all by 15 gives

9B + 15B + 25B = 147*15

49B = 2205

B = 45.

Btw., this forum is for mathematicians preparing for the GRE Subject Test, which is different from Quantitative Section of the GRE General test.