1997 AMC 8 Problem 18

Attempt Problem 18 of the 1997 AMC 8 below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

18.

At the grocery store last week, small boxes of facial tissue were priced at 44 boxes for $5.\$5. This week they are on sale at 55 boxes for $4.\$4. The percent decrease in the price per box during the sale was closest to
30%30\%
35%35\%
40%40\%
45%45\%
65%65\%
Answer: B
Concepts:percentagerate
Small hint:
Percent decrease is change divided by original price
Big hint:
Compute the old and sale prices per box
Solution:
Originally, each box is worth $5÷4=$1.25. \$ 5 \div 4 = \$ 1.25.
Now, each box is worth $4÷5=$0.8. \$ 4 \div 5 = \$ 0.8.
The percent decrease is then 1.25−0.81.25⋅100%=45125⋅100%=925⋅100%=36%. \begin{gathered} \dfrac{1.25 - 0.8}{1.25} \cdot 100 \% \\ = \dfrac{45}{125} \cdot 100 \% \\ = \dfrac{9}{25} \cdot 100 \% \\ = 36 \%. \end{gathered}
Thus, B is the correct answer.
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