A team charges 8 for each ticket and makes 1100 in concessions. The team must pay 3300. Each fan gets a free bat that costs the team $4 per bat. How many tickets must be sold to break even?

Answer 1

Hello,

To find the break-even point, we need to consider the amount of income the team receives as compared to the expenses the team incurs.

Break-Even Point = Income - Expenses = 0

Let’s deal with Income first. The team earns $8 per ticket (so 8x where x is the number of tickets sold) plus $1,100 in concessions. So Income is 8x + 1,100.

Next, we’ll deal with Expenses. The team pays $4 to give away a bat to each fan (so 4x) plus $3,300. So Expenses are 4x + 3,300.

So the break-even point = (8x + 1,100) - (4x + 3,300) = 0,

8x + 1,100 - 4x - 3,300 = 0

4x - 2,200 = 0

4x = 2,200

x = 555

The team breaks even when 555 tickets are sold.

Answer 2

Let x = number of tickets sold

Amount taken in = 8x + 1100

Costs = 4x + 3300

Break even when 8x + 1100 = 4x + 3300

4x = 2200

x = 550

In order to break even, 550 tickets must be sold.

Answer 3

For each fan, the team makes 8 for a ticket, but loses 4 for the cost of the bat: 8-4 = 4 per ticket is earned.

4t + 1100 = 3300

4t = 2200

t = 2200/4 = 550