Difference between revisions of "1997 AJHSME Problems/Problem 18"

Problem

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

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

Solution

Last week, each box was $\frac{5}{4} = 1.25$

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

Percent decrease is given by $\frac{X_{old} - X_}{X_}} \cdot 100\%$ (Error compiling LaTeX. ! Missing { inserted.)

This, the percent decrease is $\frac{1.25 - 0.8}{1.25}\cdot 100\% = \frac{45}{125} \cdot 100\% = 36\%$, which is closest to $\boxed{B}$