1988 AMC 8 Problem 23

Below is the professionally curated solution for Problem 23 of the 1988 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 8 solutions, or check the answer key.

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Concepts:ratio and proportion

Difficulty rating: 1110

23.

Maria buys computer disks at a price of $4$ for $5 and sells them at a price of $3$ for $5. How many computer disks must she sell in order to make a profit of $100?

$100$

$120$

$200$

$240$

$1200$

Solution:

Consider disks in dozens, since $12$ is a multiple of both $4$ and $3.$ A dozen disks costs $3 \times \$5 = \$15$ to buy and sells for $4 \times \$5 = \$20,$ for a profit of $5 per dozen.

To make $100 profit she needs $\dfrac{100}{5} = 20$ dozen, which is $20 \times 12 = 240$ disks.

Thus, the correct answer is D .

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