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.

$SML$

$LMS$

$MSL$

$LSM$

$MLS$

Answer: E

Concepts:percentage ratio and proportion

Difficulty rating: 1550

Small Hint:

Choose convenient numbers for the small and large sizes.

Big Hint:

Compare price per ounce for each size.

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 $S: \frac{1.00}{10}=0.100$ , $M: \frac{1.50}{16}=0.09375$ , and $L: \frac{1.95}{20}=0.0975$ .

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

Thus, E is the correct answer.

2005 AMC 8 Problem 22

Answer: E

Difficulty rating: 1550

Small Hint:

Big Hint:

Solution:

Problem 22 in Other Years