Please show me how to solve:
At the local ballpark, the team charges $5 for each ticket and expects to make $1,300 in concessions. The team must pay its players $1,800 and pay all other workers $1,500. Each fan gets a free bat that costs the team $3 per bat. How many tickets must be sold to break even?
1000
Income = $5x + 1300.
Expense = $3x + (1500+1800).
Expense = 3x + 3300.
To break even:
Income = Expense,
5x + 1300 = 3x + 3300,
Solve for X.
let the number of tickets sold be x
5x - 3x - 1300 - 1800 = 0
solve for x
Why did the ballpark decide to sell tickets to clowns? Because they needed some funny money! Now, let's crunch those numbers and make some calculations.
To break even, the team's total expenses should equal its total revenue. Let's break it down:
Expenses:
- Player Salaries: $1,800
- Other Workers: $1,500
- Bats: $3 per bat x Number of Tickets
Concessions: $1,300
Revenue:
- Ticket Sales: $5 per ticket x Number of Tickets
To find out how many tickets the team needs to sell to break even, we need to determine the number of tickets that will cover all the expenses. So, let's calculate:
Expenses = Revenue
$1,800 + $1,500 + ($3 x Number of Tickets) = $1,300 + ($5 x Number of Tickets)
$3 x Number of Tickets = $1,300 + ($5 x Number of Tickets) - ($1,800 + $1,500)
$3 x Number of Tickets = $1,300 + $5 x Number of Tickets - $3,300
$3 x Number of Tickets - $5 x Number of Tickets = $1,300 - $3,300
- $2 x Number of Tickets = - $2,000
Now, let's solve for the Number of Tickets:
Number of Tickets = (-$2,000) / (-$2)
Number of Tickets = 1,000
So, the ballpark must sell 1,000 tickets to break even. Let's hope they don't attract too many jokers.
To find out how many tickets must be sold to break even, we need to calculate the total expenses incurred by the team and then divide it by the ticket price of $5.
First, let's calculate the total expenses:
- Player payments: $1,800
- Worker payments: $1,500
- Cost of bats given to fans: $3 per bat
Now, we need to find the number of bats given to fans. To do this, we divide the total cost of bats by the cost per bat:
- Total cost of bats: $3 per bat * (number of bats given to fans)
- Since each fan gets a bat, the number of bats given to fans is equal to the number of tickets sold.
Therefore, our equation becomes:
Total Expenses = Player payments + Worker payments + (Cost per bat * Number of tickets sold)
To break even, the total expenses should be equal to the revenue earned from ticket sales and concessions. Given that the revenue from concessions is $1,300, we can set up the equation:
Total Expenses = Revenue from ticket sales + Revenue from concessions
Now, we'll substitute the variables in the equation and solve it to find the number of tickets that must be sold:
Player payments + Worker payments + (Cost per bat * Number of tickets sold) = (Ticket price * Number of tickets sold) + Revenue from concessions
Let's put the numbers into the equation and solve for Number of tickets sold:
$1,800 + $1,500 + ($3 * Number of tickets sold) = ($5 * Number of tickets sold) + $1,300
Simplifying the equation:
$3 * Number of tickets sold - $5 * Number of tickets sold = $1,300 - ($1,800 + $1,500)
- $2 * Number of tickets sold = $1,300 - $3,300
- $2 * Number of tickets sold = - $2,000
Now, divide both sides of the equation by -2 to solve for Number of tickets sold:
Number of tickets sold = (-$2,000) / (-$2)
The negatives cancel out, so:
Number of tickets sold = $1,000
Therefore, to break even, the team must sell 1,000 tickets.