2005 AMC 12B Problem 3

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?

\dfrac{1}{5}

\dfrac{1}{3}

\dfrac{2}{5}

\dfrac{2}{3}

\dfrac{4}{5}

Answer: C

Concepts:fraction ratio and proportion

Difficulty rating: 1050

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 what one third of them cost, namely

3\cdot\dfrac15 = \dfrac35

of her money.

She has

1 - \dfrac35 = \dfrac25

of her money left.

Thus, the correct answer is C.