1996 AMC 8 Problem 19

Attempt Problem 19 of the 1996 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 1996 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 pie charts below indicate the percent of students who prefer golf, bowling, or tennis at East Junior High School and West Middle School. The total number of students at East is 20002000 and at West, 2500.2500. In the two schools combined, the percent of students who prefer tennis is
30%30\%
31%31\%
32%32\%
33%33\%
34%34\%
Answer: C
Concepts:percentagemean
Small hint:
Find the actual number of tennis fans at each school, not just the percents
Big hint:
Add the two counts and divide by the total of 45004500 students
Solution:
East has 0.22⋅2000=4400.22 \cdot 2000 = 440 tennis fans, and West has 0.40⋅2500=1000.0.40 \cdot 2500 = 1000.
Together 14401440 of the 45004500 students prefer tennis, which is 14404500=32%.\dfrac{1440}{4500} = 32\%.
Thus, the correct answer is C .
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