1997 AMC 8 Problem 4

Attempt Problem 4 of the 1997 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 1997 AMC 8 solutions, or check the answer key.

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

4.

Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150150 words per minute. If Julie speaks at the ideal rate, which of the following number of words would be an appropriate length for her speech?
22502250
30003000
42004200
43504350
56505650
Answer: E
Concepts:rateunit conversion
Small hint:
Multiply the minute bounds by 150150 words per minute
Big hint:
Convert the time range into minutes
Solution:
One-half hour is 3030 minutes, in which Julie can speak 150⋅30=4500 150 \cdot 30 = 4500 words. Three-quarters of an hour is 4545 minutes, in which Julie can speak 150⋅45=6750 150 \cdot 45 = 6750 words. The only answer choice in between these two values is 5650.5650.
Thus, E is the correct answer.
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