1997 AMC 8 Problem 18

Below is the professionally curated solution for Problem 18 of the 1997 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 8 solutions, or check the answer key.

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Concepts:percentage rate

Difficulty rating: 1280

18.

At the grocery store last week, small boxes of facial tissue were priced at $4$ boxes for $\$5.$ This week they are on sale at $5$ boxes for $\$4.$ The percent decrease in the price per box during the sale was closest to

$30\%$

$35\%$

$40\%$

$45\%$

$65\%$

Solution:

Originally, each box is worth $\$ 5 \div 4 = \$ 1.25.$

Now, each box is worth $\$ 4 \div 5 = \$ .8.$

The percent decrease is then $\dfrac{1.25 - .8}{1.25} \cdot 100 \% = \dfrac{45}{125} \cdot 100 \%$ $= \dfrac{9}{25} \cdot 100 \% = 36 \%.$

Thus, B is the correct answer.

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