1999 AMC 8 Problem 18

Attempt Problem 18 of the 1999 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 1999 AMC 8 solutions, or check the answer key.

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

18.

They learn that a big concert is scheduled for the same night and attendance will be down 25%.25\%. How many recipes of cookies should they make for their smaller party?
66
88
99
1010
1111
Answer: E
Concepts:percentagefloor and ceiling functions
Small hint:
A 25%25\% drop leaves 75%75\% attendance
Big hint:
Round the needed number of recipes up
Solution:
There will now only be 108⋅(1−14)=108⋅34=81 108 \cdot \left(1 - \dfrac{1}{4}\right) = 108 \cdot \dfrac{3}{4} = 81 people at the party. This means we need ⌈81⋅215⌉=⌈16215⌉=11 \left\lceil \dfrac{81 \cdot 2}{15} \right\rceil = \left\lceil \dfrac{162}{15} \right\rceil = 11 recipes.
Thus, E is the correct answer.
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