AMC8 2003

AMC8 2003 · Q9

AMC8 2003 · Q9. It mainly tests Ratios & proportions, Area & perimeter.

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown. Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Art’s cookies sell for 60¢ each. To earn the same amount from a single batch, how much should one of Roger’s cookies cost?

四位朋友——Art、Roger、Paul 和 Trisha——烤曲奇，而且所有曲奇的厚度都相同。曲奇的形状不同，如图所示。每个人使用相同数量的面团，Art 恰好做了 12 块曲奇。 Art 的饼干每个卖 60 美分。要从一批饼干中赚取相同金额，Roger 的一个饼干应该卖多少钱？

(A) 18¢ 18美分

(B) 25¢ 25美分

(D) 75¢ 75美分

(E) 90¢ 90美分

Answer

Correct choice: (C)

正确答案：（C）

Solution

Art’s 12 cookies sell for $12 \times \$0.60 = \$7.20$. Roger’s 18 cookies should cost $\frac{\$7.20}{18} = \$0.40$ each. OR The trapezoid’s area is 12 in$^2$ and the rectangle’s area is 8 in$^2$. So the cost of a rectangle cookie should be $\frac{8}{12} \times 60\text{c} = 40\text{c}$.

Art 的 12 个饼干卖 $12 \times \$0.60 = \$7.20$。Roger 的 18 个饼干应定价 $\frac{\$7.20}{18} = \$0.40$ 每个。或者梯形面积是 12 平方英寸，矩形面积是 8 平方英寸。所以矩形饼干价格应为 $\frac{8}{12} \times 60\text{c} = 40\text{c}$。

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