Problem 27 · 2021 Math Kangaroo
Stretch
Algebra & Patterns
substitutionsum-constraint
Each shelf holds a total of 64 deciliters of apple juice. The bottles come in three different sizes: large, medium and small (see picture). How many deciliters of apple juice does a medium bottle contain?
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Answer: D — 10
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Hint 1 of 2
Let large, medium, small bottles hold L, M, S deciliters; each shelf's bottles total 64.
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Hint 2 of 2
Write one equation per shelf and solve the system for M.
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Approach: set up one equation per shelf and solve
- Counting bottles, the three shelves give 3L + 4S = 64, 2L + 2M + 3S = 64, and 4M + 6S = 64.
- Solving the system gives S = 4, L = 16 and M = 10.
- So a medium bottle contains 10 deciliters.
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