Answer:
Step-by-step explanation:
Let x represent the number of children tickets that the theatre can sell.
Let y represent the number of adult tickets that the theatre can sell.
The theater can seat up to 350 people. This means that
x + y ≤ 350
Children's tickets cost $5 each and adult tickets cost $10 each.
The theater wants to take in at least $2000 for the matinee. This means that
5x + 10y ≥ 2000 - - - - - - - - -1
Substituting x = 350 - y into equation 1, it becomes
5(350 - y) + 10y ≥ 2000
1750 - 5y + 10y ≥ 2000
5y ≥ 2000 -1750
y ≥ 250/5
y ≥ 50
Substituting y = 50 into x + y ≤ 350, it becomes
x ≤ 350 - 50
x ≤ 300
The ticket combinations are
1) 300 children tickets, 50 adult tickets
2)250 children tickets, 100 adult tickets
3)200 children tickets, 150 adult tickets
4) 150 children tickets, 200 adult tickets.
5) 100 children tickets, 250 adult tickets
