At the local ballpark, the team charges $10.00 for each ticket and expects to make $1,300.00 in concessions. The team must pay its players $ 6,800.00 and pay all other workers $1,500.00. Each fan gets a free bat that costs the team $3.00 per bat. Of the following, what is the smallest number of tickets that must be sold to break even?
(1 point)
Responses
700
700
500
500
1,000
1,000
7,500
7,500
To break even, the total revenue must equal the total expenses.
The total revenue from ticket sales can be calculated by multiplying the ticket price of $10 by the number of tickets sold (let's call it x): 10x
The total expense consists of player salaries ($6,800), worker salaries ($1,500), and the cost of bats for each fan (x*3): 6800 + 1500 + 3x
So the equation for breaking even is: 10x = 6800 + 1500 + 3x
Combining like terms: 7x = 8300
Dividing both sides by 7: x = 8300/7
Therefore, the smallest number of tickets that must be sold to break even is 1,185.71. However, since you can't sell a fraction of a ticket, the answer is 1,186.
1300 in concessions though so wouldn't it be 1000 tickets?
You're right, I apologize for the oversight.
Taking into account the $1,300 in concessions, the equation for breaking even becomes:
10x = 6800 + 1500 + 1300 + 3x
Combining like terms: 7x = 9600
Dividing both sides by 7: x = 9600/7
The smallest number of tickets that must be sold to break even is 1,371.43. Since we can't sell a fraction of a ticket, the answer is 1,372.
the concession make money not take away money
Apologies for the confusion. If the concessions make money rather than take away money, then we can subtract the $1,300 in concessions from the expenses.
The equation for breaking even would now be:
10x = 6800 + 1500 - 1300 + 3x
Combining like terms:
7x = 7000
Dividing both sides by 7:
x = 7000/7
The smallest number of tickets that must be sold to break even is 1,000. Therefore, the correct answer is 1,000 tickets.