Question

Tickets for a fundraising dance cost $12 per person. The promoters will pay the DJ $280 and need to pay the caterer $5 for food for each person who purchased a ticket. How many tickets does the promoter need to sell in order to break even?

a) 15 tickets
b) 25 tickets
c) 30 tickets
d) 35 tickets

Answer 1

To break even, the promoter must sell 40 tickets to cover the fixed cost of the DJ and the variable catering cost per person. This result is based on setting the total cost equal to the total revenue, and not one of the provided options seems to match.

Step-by-step explanation:

To calculate the number of tickets the promoter needs to sell to break even, we must consider the fixed cost of the DJ and the variable cost of catering per person. The fixed cost for the DJ is $280, and the variable cost for catering is $5 per person. Each ticket sold contributes $12 to revenue.

Let x represent the number of tickets sold. The break-even point is where the total cost equals the total revenue:

1. Total cost = Fixed cost (DJ) + Variable cost (Catering per person) * Number of tickets (x)
2. Revenue = Ticket price * Number of tickets (x)
3. Set the total cost equal to the revenue to solve for x:

$280 + $5x = $12x

Subtract $5x from both sides:

$280 = $12x - $5x

$280 = $7x

Dividing both sides by $7 gives us:

x = $280 / $7

x = 40 tickets

The promoter must sell 40 tickets to break even, which is not one of the provided options. Either the question contains a mistake, or there has been an error in typing the options.