1995 AMC 8 Problem 17

Attempt Problem 17 of the 1995 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 1995 AMC 8 solutions, or check the answer key.

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

17.

The table below gives the percent of students in each grade at Annville and Cleona elementary schools:
KK 11 22 33 44 55 66
Annville 16%16\% 15%15\% 15%15\% 14%14\% 13%13\% 16%16\% 11%11\%
Cleona 12%12\% 15%15\% 14%14\% 13%13\% 15%15\% 14%14\% 17%17\%
Annville has 100100 students and Cleona has 200200 students. In the two schools combined, what percent of the students are in grade 6?6?
12%12\%
13%13\%
14%14\%
15%15\%
28%28\%
Answer: D
Concepts:percentagemean
Small hint:
Find the number of grade-66 students at each school separately
Big hint:
Divide the combined grade-66 count by the 300300 total students
Solution:
Annville has 11%11\% of 100=11100 = 11 sixth graders, and Cleona has 17%17\% of 200=34200 = 34 sixth graders.
Combined, that is 11+34=4511 + 34 = 45 out of 300300 students, which is 45300=15%.\dfrac{45}{300} = 15\%.
Thus, the correct answer is D .
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