AMC 8 2003 Problem 10

AMC8 2003 年第 10 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. How many cookies will be in one batch of Trisha's cookies?

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。 Trisha 用这批面团能做多少块饼干？

A.10
B.12
C.16
D.18
E.24

正确答案 · Correct Answer

解析 · Solution

Solution 1

Art's cookies have areas of

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

. There are 12 cookies in one of Art's batches so everyone used

12 \cdot 12=144 \text{ in}^2

of dough. Trisha's cookies have an area of

\displaystyle \frac{3 \cdot 4}{2} = 6

so she has

\displaystyle \frac{144}{6} = 24

cookies per batch.

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