AlgebraVery hardSystem of inequalities in context: which combination is allowed
Algebra practice question
A bakery has at most 12 hours of oven time and at most 20 kilograms of flour today. A batch of bread needs 2 hours and 4 kilograms; a batch of cakes needs 3 hours and 2 kilograms. Which combination of bread batches and cake batches is possible?
- A. 3 bread and 2 cakesCorrect
- B. 4 bread and 2 cakes
- C. 2 bread and 3 cakes
- D. 1 bread and 4 cakes
Answer: A. 3 bread and 2 cakes
3 bread and 2 cakes: hours 6 + 6 = 12 ≤ 12 ✓; flour 12 + 4 = 16 ≤ 20 ✓.
Why the other answers are wrong
- B. 4 bread and 2 cakes
- 4 bread and 2 cakes: hours 8 + 6 = 14 > 12.
- C. 2 bread and 3 cakes
- 2 bread and 3 cakes: hours 4 + 9 = 13 > 12.
- D. 1 bread and 4 cakes
- 1 bread and 4 cakes: hours 2 + 12 = 14 > 12.
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