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.

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

Solution

WLOG (Without Loss of Generality), suppose the small size costs $\textdollar 1$ and has $5$ oz. The medium size then costs $\textdollar 1.50$ and has $8$ oz. The large size costs $\textdollar 1.95$ and has 10 oz. The small, medium, and large sizes cost, respectively, $0.200,$ 0.188, and S0.195 per oz. The sizes from best to worst buy are $\boxed{\textbf{(E)}\ \text{MLS}}$ .

~Edits by WrenMath

Video Solution

https://www.youtube.com/watch?v=65cfokoNyfA ~David

2005 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

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2005 AMC 8 Problems/Problem 22

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Problem

Solution

Video Solution

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