AlgebraVery hardLeast number of standard tickets for a revenue target
Algebra practice question
A theatre sells standard tickets at 20 dollars and premium tickets at 50 dollars, and it can sell at most 500 tickets in total. It needs revenue of at least 12,000 dollars. If it sells exactly 100 premium tickets, what is the least number of standard tickets it must sell?
Answer: 350
20x + 5000 ≥ 12000 gives x ≥ 350, and 350 + 100 = 450 is within the 500-ticket limit.
Common wrong answers
- If you answered 250
- 250 uses 7000/28, a slip.
- If you answered 400
- 400 is the room left under the 500 limit, not the minimum needed.
- If you answered 600
- 600 ignores the premium revenue.
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