2005 AMC 8 Problem 22
Attempt Problem 22 of the 2005 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 2005 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs more than the small size and contains less detergent than the large size. The large size contains twice as much detergent as the small size and costs more than the medium size. Rank the three sizes from best to worst buy.
Answer: E
Small hint:
Choose convenient numbers for the small and large sizes.
Big hint:
Compare price per ounce for each size.
Solution:
Choose convenient values: let the small box cost and contain ounces. Then the large box contains ounces.
The medium box costs and contains less than the large box, or ounces. The large box costs more than the medium, or .
The costs per ounce are , , and .
From best to worst buy, the order is .
Thus, E is the correct answer.
Problem 22 in other years
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