Problem 20 · 2016 Math Kangaroo
Medium
Algebra & Patterns
sum-constraintcasework
There are 20 students in total, girls and boys, in a class. Two students always share a desk. One third of the boys share a desk with a girl, and half of the girls share a desk with a boy. How many boys are in the class?
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Answer: B — 12
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Hint 1 of 3
Let b boys and g girls with b + g = 20; count the mixed desks two ways.
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Hint 2 of 3
One third of the boys equals half the girls: b/3 = g/2.
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Hint 3 of 3
Solve b/3 = g/2 together with b + g = 20.
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Approach: count the mixed desks two ways
- Let b boys and g girls, b + g = 20.
- Mixed desks from the boys' side = b/3; from the girls' side = g/2; these are equal, so b/3 = g/2.
- Then 2b = 3g; with b + g = 20 this gives b = 12, g = 8, so there are 12 boys.
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