Problem 23 · 2016 Math Kangaroo
Stretch
Algebra & Patterns
sum-constrainttotal-then-divide
Twelve girls met up in a pastry shop. On average they each ate 1.5 muffins. None of them ate more than two muffins, and two of them ate nothing. How many girls ate two muffins?
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Answer: E — 8
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Hint 1 of 2
Twelve girls averaging 1.5 muffins ate 18 muffins total.
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Hint 2 of 2
Two ate 0; of the other 10 let x eat 2 and the rest 1, then use the total 18.
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Approach: set up the total-muffin equation
- Total muffins = 12 × 1.5 = 18.
- Two girls ate 0; of the remaining 10 let x eat 2 and (10 − x) eat 1: 2x + (10 − x) = 18.
- Then x + 10 = 18, so x = 8 girls ate two muffins.
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