2004 AMC 8 Problem 3

Attempt Problem 3 of the 2004 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 2004 AMC 8 solutions, or check the answer key.

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

3.

Twelve friends met for dinner at Oscar’s Overstuffed Oyster House, and each ordered one meal. The portions were so large, there was enough food for 1818 people. If they shared, how many meals should they have ordered to have just enough food for the 1212 of them?
88
99
1010
1515
1818
Answer: A
Concepts:ratio and proportion
Small hint:
The 1212 meals made enough food for 1818 people.
Big hint:
Find how many meals are needed per person, then scale to 1212 people.
Solution:
Note that 1212 meals feed 1818 people. This means that one meal feeds 1812=32\dfrac{18}{12} = \dfrac{3}{2} people.
This means that they need 12÷32=812 \div \dfrac{3}{2} = 8 meals for 1212 people.
Thus, A is the correct answer.
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