Final answer:
To meet the target revenue of $3,500, the theater must sell a minimum of 154 tickets at $20 each. The total revenue is calculated by multiplying the number of tickets sold at each price by their respective prices. By considering the maximum number of discounted tickets and setting up an inequality, we can find the minimum value of the other variable.
Step-by-step explanation:
To calculate the minimum ticket sales required to meet the target revenue, we need to consider the different ticket prices and the maximum number of seats. Let's assume the number of tickets sold at $20 is x and the number of discounted tickets sold at $14 is y.
The total revenue can be calculated as follows: Total Revenue = ($20 * x) + ($14 * y)
Since the theater must make at least $3,500, we can set up the following inequality to find the minimum number of tickets sold:
($20 * x) + ($14 * y) ≥ $3,500
Now, let's use the given information that a maximum of 10% of the total seats can be discounted tickets. If there are 300 seats in total, the maximum number of discounted tickets can be calculated as follows: y ≤ 0.1 * 300 = 30
By substituting the value of y in the inequality, we can find the minimum value of x:
($20 * x) + ($14 * 30) ≥ $3,500
($20 * x) + ($420) ≥ $3,500
($20 * x) ≥ $3,080
x ≥ $3,080 / $20
x ≥ 154
Therefore, the minimum number of tickets sold at $20 should be at least 154 in order to meet the target revenue of $3,500.