Problem 18 · 2014 Math Kangaroo
Medium
Algebra & Patterns
substitutionsum-constraint
A chess player plays 40 matches and gains 25 points from them, where a win gives 1 point, a draw 12 point, and a loss 0 points. How many more matches does he win than he loses?
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Answer: C — 10
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Hint 1 of 2
Set up wins, draws, losses with the match-count and points equations.
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Hint 2 of 2
Subtract the equations cleverly to get wins minus losses directly.
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Approach: combine the total-games and total-points equations
- Let w, d, l be wins, draws, losses: w + d + l = 40 and w + d/2 = 25.
- Double the second: 2w + d = 50; subtract the first: w − l = 10.
- He wins 10 more matches than he loses.
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