AMC 8 2005 Problem 22

AMC8 2005 年第 22 题

比与比例★★★☆☆

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.

一家公司卖三种不同大小的盒子包装的洗涤剂：小盒子（S）、中盒子（M）和大盒子（L）。中号比小号贵 50％，且洗涤剂含量比大号少 20％．大号的洗涤剂含量是小号的两倍，价格比中号高 30％。请将这三种不同尺寸的洗涤剂按照性价比从高到低排列。

A. $\text{SML}$
B. $\text{LMS}$
C. $\text{MSL}$
D. $\text{LSM}$
E. $\text{MLS}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

WLOG (Without Loss of Generality), suppose the small size costs $1 and has 5 oz. The medium size then costs $1.50 and has 8 oz. The large size costs $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

\text{MLS}

. by WrenMath

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