Final answer:
The theater needs to sell 931 child tickets at $5 each to reach their $5000 profit goal if they have already sold 23 adult tickets at $15 each. The equation is $5000 = 23 × $15 + C × $5, which simplifies to C = 931. The graph would show the different combinations of adult and child tickets that meet the profit goal, using intercepts (0,931) and (333,0).
Step-by-step explanation:
Solving the Ticket Sales Problem
To solve the community theater's problem, we need to write an equation that represents the total profit from selling adult and child tickets. Let's define adult tickets as A and child tickets as C. We are given that the theater sells adult tickets at $15 each and child tickets at $5 each, with the goal of making a profit of $5000. Additionally, they have sold 23 adult tickets already.
The equation representing the total profit would be:
Profit = (Number of Adult Tickets sold) × (Price per Adult Ticket) + (Number of Child Tickets sold) × (Price per Child Ticket)
Putting the given numbers into the equation:
$5000 = 23 × $15 + C × $5
To find how many child tickets need to be sold, we can simplify the equation:
$5000 = $345 + $5C
$5000 - $345 = $5C
$4655 = $5C
Dividing both sides by $5, we get:
C = 931
Thus, the theater needs to sell 931 child tickets to reach their goal of $5000.
To graph this equation using the intercepts, we would plot the point (0,931) where only child tickets are sold and the point (333,0) where only adult tickets are sold, along the line representing different combinations of adult and child tickets that total $5000 in profit.