2002 AMC 8 Problem 10

Attempt Problem 10 of the 2002 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 2002 AMC 8 solutions, or check the answer key.

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

10.

The average price of his ‘7070s stamps is closest to
3.53.5¢
44¢
4.54.5¢
55¢
5.55.5¢
Answer: E
Concepts:data and graph interpretationmean
Small hint:
Compute the total cost of all ‘7070s stamps.
Big hint:
Divide the total cost by the number of ‘7070s stamps, then choose the closest option.
Solution:
The ‘7070s stamps cost 12⋅6+12⋅6+6⋅4+13⋅5=72+72+24+65=233 \begin{aligned} &12\cdot6+12\cdot6 \\ &\quad {}+6\cdot4+13\cdot5 \\ &\quad {}=72+72+24+65 \\ &\quad {}=233 \end{aligned} cents.
There are 12+12+6+13=4312+12+6+13=43 stamps, so the average cost is 233÷43,233\div43, a little more than 55 cents and closest to 5.55.5 cents.
Thus, E is the correct answer.
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