Problem:
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:
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- Roger's cookies are rectangles:
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- Paul's cookies are parallelograms:
- Trisha's cookies are triangles:
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Each friend uses the same amount of dough, and Art makes exactly cookies.
Art's cookies sell for each. To earn the same amount from a single batch, how much should one of Roger's cookies cost?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Art's cookies sell for . Roger's cookies should cost each.
The trapezoid's area is and the rectangle's area is . So the cost of a rectangle cookie should be .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions