Problem 24 · 2012 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintcasework
In football you get 3 points for a win, no points for a loss, and 1 point for a draw. A team has played 36 matches and has 80 points. What is the maximum number of matches the team could have lost?
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Answer: E — 8
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Hint 1 of 2
A loss is worth 0 points, so the more games lost, the fewer games are left to earn all 80 points.
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Hint 2 of 2
Wins are worth the most (3 each), so packing the points into wins leaves the most room for losses.
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Approach: earn the 80 points in as few games as possible, then the rest are losses
- Losses give 0 points, so all 80 points must come from the wins and draws — and the fewer of those games, the more games are free to be losses.
- Wins are worth 3 and draws only 1, so use mostly wins: 26 wins make 26 × 3 = 78 points, then 2 draws add 2 more for exactly 80.
- That uses 26 + 2 = 28 games, leaving 36 − 28 = 8 games to lose.
- So the most matches the team could have lost is 8.
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