Problem 17 · 2021 Math Kangaroo
Medium
Algebra & Patterns
Arithmetic & Operations
substitutioncasework
There are 20 questions in a quiz. Each correct answer scores 7 points, each wrong answer scores −4 points, and each question left blank scores 0 points. Eric took the quiz and scored 100 points. How many questions did he leave blank?
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Answer: B — 1
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Hint 1 of 2
Let the numbers of correct, wrong and blank answers add to 20, with score 7c − 4w = 100.
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Hint 2 of 2
Search for whole-number solutions and read off the blanks.
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Approach: solve the score equation in whole numbers
- With c correct and w wrong: 7c − 4w = 100 and c + w ≤ 20.
- c = 16, w = 3 gives 112 − 12 = 100, and that is the only fit.
- Then blanks = 20 − 16 − 3 = 1.
- So the answer is B.
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