2003 AMC 8 Problem 9

Attempt Problem 9 of the 2003 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

9.

Art’s cookies sell for 6060¢ each. To earn the same amount from a single batch, how much should one of Roger’s cookies cost?
1818¢
2525¢
4040¢
7575¢
9090¢
Answer: C
Concepts:arearatio and proportion
Small hint:
First find the total money Art earns from a batch.
Big hint:
Use the number of Roger’s cookies from the shared dough amount.
Solution:
Art makes 1212 cookies that sell for 6060 cents each, so one batch earns 12⋅60=72012\cdot60=720 cents.
The batch has 12⋅12=14412\cdot12=144 square inches of dough area, and each Roger cookie has area 4⋅2=8.4\cdot2=8. Thus Roger makes 144÷8=18144\div8=18 cookies.
To earn 720720 cents from 1818 cookies, each Roger cookie should cost 720÷18=40720\div18=40 cents.
Thus, C is the correct answer.
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