2012 AMC 8 Problem 1

Attempt Problem 1 of the 2012 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 8 solutions, or check the answer key.

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

1.

Rachelle uses 33 pounds of meat to make 88 hamburgers for her family. How many pounds of meat does she need to make 2424 hamburgers for a neighborhood picnic?
6 6
623 6\dfrac23
712 7\dfrac12
8 8
9 9
Answer: E
Concepts:ratio and proportion
Small hint:
Scale from 88 hamburgers to 2424 hamburgers.
Big hint:
The hamburger count triples, so the meat amount triples.
Video solution:
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Written solution:
If we have 88 hamburgers, we have 13\dfrac{1}{3} of the 2424 hamburgers. This means we have 13\dfrac{1}{3} of the meat when we have 33 pounds. The total amount of meat is therefore 113⋅3=3⋅3=9.\dfrac{1}{\dfrac{1}{3}} \cdot 3 = 3\cdot3 = 9.
Thus, the answer is E .
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