2005 AMC 10B Problem 5

Question

Brianna is using part of the money she earned on her weekend job to buy several equally-priced CDs. She used one fifth of her money to buy one third of the CDs. What fraction of her money will she have left after she buys all the CDs?

\dfrac15

\dfrac13

\dfrac25

\dfrac23

\dfrac45

Answer: C

Concepts:fraction ratio and proportion money

Difficulty rating: 960

Small hint:

Buying all the CDs costs three times as much as buying one third of them

Big hint:

All the CDs cost

3\cdot\dfrac15

of her money

Solution:

Buying all the CDs costs three times as much as buying one third of them, namely

3 \cdot \dfrac15 = \dfrac35

of her money.

The fraction left over is

1 - \dfrac35 = \dfrac25.

Thus, C is the correct answer.