Tickets for a community theater production cost $6 each when bought in advance
Tickets for a community theater production cost $6 each when bought in advance and $8 each when bought at the door. The theater group’s goal is at least $2,000 in ticket sales for opening night. The theater group sold 142 opening-night tickets in advance. What is the minimum number of tickets they need to sell at the door on opening night to make their goal?
- 143
- 144
- 192
- 250
- 357
Answer
The amount collected from the sale of 142 tickets bought in advance is equal to ($6 per ticket)(142 tickets) = $852.
The amount collected from the sale of d tickets bought at the door is equal to ($8 per ticket)(d tickets) = $8d.
The total amount collected from all ticket sales is 852 + 8d.
To determine the minimum number of tickets to produce $2,000 in ticket sales, you can set up an inequality:
852 + 8d ≥ 2,000
Subtracting 852 from both sides and then dividing by 8 produces the equivalent inequality
d ≥ 143.5
The d must be a whole number of tickets, so you must select the whole number d to satisfy the inequality. This means you must round 143.5 up to obtain the correct answer.