AMC8 2005

AMC8 2005 · Q22

AMC8 2005 · Q22. It mainly tests Percent, Rounding & estimation.

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:

一家公司销售三种不同尺寸的洗涤剂盒子：小号(S)、中号(M)和大号(L)。中号的价格是小号的50%更高，包含的洗涤剂比大号少20%。大号包含的洗涤剂是小号的两倍，价格是中号的30%更高。将三种尺寸从最佳购买到最差购买排名：

(A) SML SML

(B) LMS LMS

(D) LSM LSM

(E) MLS MLS

Answer

Correct choice: (E)

正确答案：（E）

Solution

(E) Neither the units of size nor the cost are important in this problem. So for convenience, suppose the small size costs \$1 and weighs 10 ounces. To determine the relative value, we compare the cost per unit weight. $S:\ \dfrac{\$1.00}{10}=10\text{¢ per oz.}$ $M:\ \dfrac{\$1.50}{0.8\times 20}=9.375\text{¢ per oz.}$ $L:\ \dfrac{1.3\times \$1.50}{20}=9.75\text{¢ per oz.}$ So the value, or buy, from best to worst is medium, large and small, that is MLS.

（E）在这个问题中，尺寸的单位和价格单位都不重要。为方便起见，假设小号价格为 \$1，重量为 10 盎司。为了确定相对性价比，我们比较单位重量的成本。 $S:\ \dfrac{\$1.00}{10}=10\text{¢/盎司}$ $M:\ \dfrac{\$1.50}{0.8\times 20}=9.375\text{¢/盎司}$ $L:\ \dfrac{1.3\times \$1.50}{20}=9.75\text{¢/盎司}$ 因此，从最划算到最不划算的购买顺序是：中号、大号、小号，即 MLS。

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