2005 AMC 10B Problem 5

Below is the professionally curated solution for Problem 5 of the 2005 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 10B solutions, or check the answer key.

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Concepts:fraction ratio and proportion money

Difficulty rating: 960

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?

$\dfrac15$

$\dfrac13$

$\dfrac25$

$\dfrac23$

$\dfrac45$

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.

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