2005 AMC 12B Problem 3

Below is the professionally curated solution for Problem 3 of the 2005 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12B solutions, or check the answer key.

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Concepts:fractionratio and proportion

Difficulty rating: 1050

3.

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?

15\dfrac{1}{5}

13\dfrac{1}{3}

25\dfrac{2}{5}

23\dfrac{2}{3}

45\dfrac{4}{5}

Solution:

Buying all the CDs costs three times what one third of them cost, namely 315=353\cdot\dfrac15 = \dfrac35 of her money.

She has 135=251 - \dfrac35 = \dfrac25 of her money left.

Thus, the correct answer is C.

Problem 3 in Other Years