Question

Problems $8, 9,$ and $10$ use the data found in the accompanying paragraph and figures.

Bake Sale

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 cookies are rectangles:

• Paul's cookies are parallelograms:

• Trisha's cookies 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?

$\text{Art}$

$\text{Paul}$

$\text{Roger}$

$\text{Trisha}$

$\text{There is a tie for fewest.}$

Solution:

Since the cookies all have the same thickness and use the same amount of dough, the largest cookie shape produces the fewest cookies.

Art’s trapezoid has area $\frac12(3+5)\cdot3=12$ . Roger’s rectangle has area $4\cdot2=8$ . Paul’s parallelogram has area $3\cdot2=6$ , and Trisha’s triangle has area $\frac12\cdot3\cdot4=6$ .

Art has the largest cookie area, so Art gets the fewest cookies from one batch.

Thus, A is the correct answer.

2003 AMC 8 Problem 8

Solution:

Problem 8 in Other Years