A drama club wants to raise at least $500 in ticket sales for its annual show. The members of the club sold 50 tickets at a special rate of $5. The usual ticket price the day of the show is $7.50. At least how many tickets do they need to sell the day of the show to meet the goal?
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $8 and each adult ticket sells for $11.50. The auditorium can hold at most 81 people. The drama club must make at least $760 from ticket sales to cover the show's costs. If 43 student tickets were sold, determine the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses. If there are no possible solutions, submit an empty answer.
500 - (50 * 5) = 250
250 / 7.5 = ________ tickets
33.3333
To determine how many tickets the drama club needs to sell the day of the show to meet the goal, we need to calculate the remaining amount needed to reach $500 and then divide it by the price difference between the special rate and the usual ticket price.
First, let's calculate the total amount collected from the sale of 50 tickets at the special rate of $5:
50 tickets * $5 per ticket = $<<50*5=250>>250
Now we need to determine the remaining amount needed to reach the goal:
Target amount - Amount collected = Remaining amount needed
$500 - $250 = $<<500-250=250>>250
Next, we'll calculate the number of tickets they need to sell at the usual ticket price of $7.50 to cover the remaining amount needed. To do this, we'll divide the remaining amount by the price difference between the special rate and the usual ticket price:
Remaining amount needed / Price difference = Number of tickets required
$250 / ($7.50 - $5) = $250 / $2.50 = <<250/2.50=100>>100
Therefore, the drama club needs to sell at least 100 tickets at the usual ticket price of $7.50 to meet their goal of raising at least $500.