2005 AMC 8 Problems/Problem 22

Problem

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.

$\textbf{(A)}\ \text{SML}\qquad\textbf{(B)}\ \text{LMS}\qquad\textbf{(C)}\ \text{MSL}\qquad\textbf{(D)}\ \text{LSM}\qquad\textbf{(E)}\ \text{MLS}$

Solution

Suppose the small size costs $\textdollar 1$ and the large size has $10$ oz. The medium size then costs $\textdollar 1.50$ and has $8$ oz. The small size has $5$ oz and the large size costs $\textdollar 1.95$ . The small, medium, and large size cost respectively, $0.200, 0.188, 0.195$ dollars per oz. The sizes from best to worst buy are $\boxed{\textbf{(E)}\ \text{MLS}}$ .

2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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2005 AMC 8 Problems/Problem 22

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