At the local ballpark, the team charges 4$ for each ticket and expects to make 1200$ in concessions. The team must pay its players 2100$ And pay all other workers 1900$. Each fan gets a free bat that costs the team 3$ per bat. How many tickets must be sold to break even?
Well, revenue must equal costs, so if they sell t tickets and f fans get free bats, we have
4t + 1200 = 2100+1900+3f
To determine how many tickets must be sold to break even, we need to consider the expenses and revenues of the baseball team.
Let's break down the information provided:
- The team charges $4 for each ticket sold.
- The team expects to make $1200 in concessions.
- The team must pay its players $2100.
- The team must pay all other workers $1900.
- Each fan gets a free bat that costs the team $3 per bat.
To calculate the total expenses of the team, we sum up the player salaries, worker salaries, and the cost of bats:
Total Expenses = Player Salaries + Worker Salaries + (Cost of Bats * Number of Tickets Sold)
The revenue of the team will be the sum of the ticket sales and the concession sales:
Total Revenue = (Ticket Price * Number of Tickets Sold) + Concessions
To break even, the total revenue should be equal to the total expenses:
Total Revenue = Total Expenses
Now, let's calculate the number of tickets that need to be sold to break even:
1. Set up the equation by substituting the given values:
(4 * Number of Tickets Sold) + 1200 = 2100 + 1900 + (3 * Number of Tickets Sold)
2. Simplify the equation:
4 * Number of Tickets Sold + 1200 = 4000 + 3 * Number of Tickets Sold
3. Combine like terms:
4 * Number of Tickets Sold - 3 * Number of Tickets Sold = 4000 - 1200
4. Simplify further:
Number of Tickets Sold = 2800 / 1
5. Solve for the number of tickets:
Number of Tickets Sold = 2800
So, to break even, the team must sell 2800 tickets.