Question

A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs $50 \%$ more than the small size and contains $20 \%$ less detergent than the large size. The large size contains twice as much detergent as the small size and costs $30 \%$ more than the medium size. Rank the three sizes from best to worst buy.

$SML$

$LMS$

$MSL$

$LSM$

$MLS$

Solution:

Choose convenient values: let the small box cost $\$1.00$ and contain $10$ ounces. Then the large box contains $20$ ounces.

The medium box costs $\$1.50$ and contains $20\%$ less than the large box, or $16$ ounces. The large box costs $30\%$ more than the medium, or $\$1.95$ .

The costs per ounce are $S: 1.00/10=0.100$ , $M: 1.50/16=0.09375$ , and $L: 1.95/20=0.0975$ .

From best to worst buy, the order is $M,L,S$ .

Thus, E is the correct answer.

2005 AMC 8 Problem 22

Solution:

Problem 22 in Other Years