Problem 16 · 1987 AJHSME
Hard
Fractions, Decimals & Percents
set-up-percent-equation
Joyce made 12 of her first 30 shots in the first three games of this basketball game, so her seasonal shooting average was 40%. In her next game, she took 10 shots and raised her seasonal shooting average to 50%. How many of these 10 shots did she make?
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Answer: E — 8.
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Hint 1 of 2
A season average is about totals, not single games. Work out her total makes before and after the new game, and the difference is what you want.
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Hint 2 of 2
After the extra game she's taken 30 + 10 = 40 shots at a 50% average. How many total baskets does that mean — and how many had she already made?
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Approach: work in season totals, then take the difference
- An average is (total made) ⁄ (total shots), so work with totals. After the game she's taken 40 shots at 50%, meaning 50% × 40 = 20 total makes.
- She'd already made 12, so this game she made 20 − 12 = 8.
- Why this transfers: never average the averages or work game-by-game — convert each percentage back to a count of makes over a count of shots, then subtract. Totals are what actually add up.
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