1990 AMC 8 Problem 17

Attempt Problem 17 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).

17.

A straight concrete sidewalk is to be 33 feet wide, 6060 feet long, and 33 inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?
22
55
1212
2020
more than 2020
Answer: A
Concepts:volumeunit conversion
Small hint:
First convert 33 inches to feet: 3 in=14 ft3 \text{ in} = \dfrac14 \text{ ft}
Big hint:
Find the volume in cubic feet, then divide by 2727 since 11 cubic yard =27= 27 cubic feet
Solution:
The thickness is 33 inches =14= \dfrac14 foot, so the volume is 3⋅60⋅14=453 \cdot 60 \cdot \dfrac14 = 45 cubic feet.
Since 11 cubic yard =27= 27 cubic feet, this is 4527=123\dfrac{45}{27} = 1\dfrac23 cubic yards. Rounding up to a whole number, the contractor must order 22 cubic yards.
Thus, the correct answer is A .
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