Problem 17 · 1995 AJHSME
Hard
Fractions, Decimals & Percents
weighted-percent
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Answer: D — 15%.
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Hint 1 of 2
The two schools are different sizes, so you can't just average 11% and 17%. A percent of 100 students and a percent of 200 students mean different numbers of kids — convert to actual kids first.
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Hint 2 of 2
Turn each grade-6 percent into a head count, add the counts, then take that over the 300 total.
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Approach: convert to head counts (the schools have different sizes), then one combined percent
- The trap is averaging 11% and 17% to get 14%. That's wrong because Cleona has twice as many students — its percentage should count double. So switch to real counts.
- Grade 6 counts: Annville 11% of 100 = 11 kids; Cleona 17% of 200 = 34 kids. Together 45 kids.
- Out of all 300 students that's 45300 = 15%.
- Why this transfers: this is a weighted average — percentages can only be combined directly when the groups are the same size. Different sizes → count the actual items, then re-percent at the end. (Notice 15% leans toward Cleona's 17%, because Cleona is the bigger school.)
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