AMC 8 2003 Problem 9

AMC8 2003 年第 9 题

比与比例★★☆☆☆

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown: Art's cookies are trapezoids, Roger's are rectangles, Paul's are parallelograms, and Trisha's are triangles. 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 one batch of dough, how much should one of Roger's cookies cost?

四位朋友 Art、Roger、Paul 和 Trisha 一起烤饼干，所有饼干厚度相同，但形状不同（如图）：Art 的是梯形，Roger 的是矩形，Paul 的是平行四边形，Trisha 的是三角形。每位朋友用的面团一样多，且 Art 恰好做了 12 块饼干。 Art 的饼干每个卖 60 美分。为了从这批面团赚得同样的钱，Roger 的饼干应该每个卖多少美分？

A.18
B.25
C.40
D.75
E.90

正确答案 · Correct Answer

解析 · Solution

Solution 1

The area of one of Art's cookies is

\displaystyle 3 \cdot 3 + \frac{2 \cdot 3}{2} = 9 + 3 = 12

. As he has 12 cookies in a batch, the amount of dough each person used is

12 \cdot 12=144

. Roger's cookies have an area of

\displaystyle \frac{144}{2 \cdot 4} = \frac{144}{8} = 18

cookies in a batch. In total, the amount of money Art will earn is

12 \cdot 60=720

. Thus, the amount Roger would need to charge per cookie is

\displaystyle \frac{720}{18} = 40

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