1990 AMC 8 Problem 13

Attempt Problem 13 of the 1990 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 1990 AMC 8 solutions, or check the answer key.

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

13.

One proposal for new postage rates for a letter was 3030¢ for the first ounce and 2222¢ for each additional ounce (or fraction of an ounce). The postage for a letter weighing 4.54.5 ounces was
9696¢
$1.07\$1.07
$1.18\$1.18
$1.20\$1.20
$1.40\$1.40
Answer: C
Concepts:ratefloor and ceiling functions
Small hint:
The first ounce costs 3030¢; the remaining 3.53.5 ounces are billed as full additional ounces
Big hint:
A fraction of an ounce counts as a whole additional ounce, so 3.53.5 ounces beyond the first counts as 44
Solution:
The first ounce costs 3030¢. The remaining 3.53.5 ounces are charged as 44 additional ounces, since any fraction rounds up to a full ounce.
That is 4⋅224 \cdot 22¢ =88= 88¢, so the total is 3030¢ +88+ 88¢ =118= 118¢ =$1.18.= \$1.18.
Thus, the correct answer is C .
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