AMC 8 2003 Problem 8

AMC8 2003 年第 8 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. Who gets the fewest cookies from one batch of cookie dough?

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。用一批面团，谁做出的饼干最少？

A. $\text{Art}$
B. $\text{Roger}$
C. $\text{Paul}$
D. $\text{Trisha}$
E. $\text{There is a tie for fewest.}$ / 并列最少

正确答案 · Correct Answer

解析 · Solution

Solution 1

Out of all the cookies, Art's has an area of

12 \text{ in}^2

, which was the greatest area out of all the cookies' areas. Roger's cookie had an area of

8 \text{ in} ^2

, and both Paul and Trisha's cookies had an area of

6 \text{ in}^2

. This means

\text{Art}

makes the fewest cookies, since his cookie area is the greatest. The answer is not that there is a tie between Paul and Trisha because they can make the most cookies with a given amount of cookie dough, not the least.

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