# 1997 AJHSME Problems/Problem 18

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## Problem

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

$\text{(A)}\ 30\% \qquad \text{(B)}\ 35\% \qquad \text{(C)}\ 40\% \qquad \text{(D)}\ 45\% \qquad \text{(E)}\ 65\%$

## Solution

Last week, each box was $\frac{5}{4} = 1.20$

This week, each box is $\frac{4}{5} = 0.80$

Percent decrease is given by $\frac{X_{old} - X_{new}}{X_{old}} \cdot 100\%$

This, the percent decrease is $\frac{1.2 - 0.8}{1.2}\cdot 100\% = \frac{1}{3} \cdot 100\% \approx 33.33\%$, which is closest to $\boxed{B}$

 1997 AJHSME (Problems • Answer Key • Resources) Preceded byProblem 17 Followed byProblem 19 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions