1999 AMC 8 Problem 19

Attempt Problem 19 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).

19.

The drummer gets sick. The concert is cancelled. Walter and Gretel must make enough pans of cookies to supply 216216 cookies. There are 88 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be left over, of course.)
55
66
77
88
99
Answer: B
Concepts:unit conversionfloor and ceiling functions
Small hint:
First round the number of pans up
Big hint:
Convert tablespoons of butter to sticks and round up
Solution:
To make 216216 cookies, they have to make ⌈21615⌉=15 \left\lceil \dfrac{216}{15} \right\rceil = 15 pans. Since each pan requires 33 tablespoons of butter, all the pans will need 15⋅3=4515 \cdot 3 = 45 tablespoons.
They will then need ⌈458⌉=6 \left\lceil \dfrac{45}{8} \right\rceil = 6 sticks of butter.
Thus, B is the correct answer.
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