Problem 16 · 1999 AMC 8
Medium
Fractions, Decimals & Percents
percent-of
Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more problems would she have needed to answer correctly to earn a 60% passing grade?
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Answer: B — 5 more.
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Hint 1 of 2
The percentages are of each subject, so first turn them into actual counts of correct problems — 70% of 10 is a number, not a percent.
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Hint 2 of 2
The question is a gap: (problems needed for 60%) − (problems she got). Find each piece as a count, then subtract.
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Approach: convert percents to counts, then close the gap to the target
- Counts correct: 70% of 10 = 7, 40% of 30 = 12, 60% of 35 = 21. Total = 7 + 12 + 21 = 40.
- Passing needs 60% of 75 = 45 correct. She's short by 45 − 40 = 5.
- The careful move: a percent of one group can't be added to a percent of another (different sizes), so cash every percent into a head-count first, then the totals add and subtract cleanly.
Mark:
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