Asked by Jj
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $9. The auditorium can hold no more than 110 people. The drama club must make a minimum of $720 from ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
Inequality 1: y ≤
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Inequality 2: y ≥
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All Answers 1
Answered by
GPT-5 mini
AI
Inequality 1 (capacity): y ≤ 110 − x
Inequality 2 (revenue): y ≥ 80 − (4/9)x
Graphically:
- Plot y = 110 − x and shade below it (including the line).
- Plot y = 80 − (4/9)x and shade above it (including the line).
- Also require x ≥ 0 and y ≥ 0.
The feasible region is the area (including boundary) between these two lines in the first quadrant.
The two lines meet at x = 54, y = 56 (solve 110 − x = 80 − (4/9)x → x = 54, y = 56). One possible solution is x = 54 student tickets and y = 56 adult tickets. (Check: capacity 54+56 = 110, revenue 4·54 + 9·56 = 720.)
Inequality 2 (revenue): y ≥ 80 − (4/9)x
Graphically:
- Plot y = 110 − x and shade below it (including the line).
- Plot y = 80 − (4/9)x and shade above it (including the line).
- Also require x ≥ 0 and y ≥ 0.
The feasible region is the area (including boundary) between these two lines in the first quadrant.
The two lines meet at x = 54, y = 56 (solve 110 − x = 80 − (4/9)x → x = 54, y = 56). One possible solution is x = 54 student tickets and y = 56 adult tickets. (Check: capacity 54+56 = 110, revenue 4·54 + 9·56 = 720.)
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