Problem 14 · 1995 AJHSME
Medium
Fractions, Decimals & Percents
percent-target
A team won 40 of its first 50 games. How many of the remaining 40 games must this team win so that it will have won exactly 70% of its games for the season?
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Answer: B — 23.
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Hint 1 of 2
The 70% is of the WHOLE season, not the remaining games. So first figure out how many total wins 70% demands; that target is the anchor for everything else.
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Hint 2 of 2
Find the target total wins for the full 90-game season, then subtract the wins the team already banked.
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Approach: find the season's target win count, then subtract what's already won
- Work backward from the goal: the team wants 70% of the entire season, and the season is 50 + 40 = 90 games. So the target is 70% of 90 = 63 wins.
- It already has 40 wins, so it still needs 63 − 40 = 23 more.
- The trap to avoid: 70% applies to all 90 games, not just the last 40 — anchoring on the season total keeps you out of that mistake.
- Sanity check: 23 of the remaining 40 is a bit over half — reasonable, since the team is already winning 40/50 = 80% and needs to dip toward 70% overall.
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