The Lakewood baseball team is selling T-shirts for a fundraiser. The shirts cost $100 for the printing design and setup, plus $10 per shirt. The team is going to sell the shirts for $15 each. How many shirts do they need to sell to break even
To break even, the total revenue from the sale of the shirts must be equal to the total cost of producing them. Let's call the number of shirts sold "x".
The cost to produce x shirts is:
$100 (printing and design cost) + $10 per shirt (production cost) x x shirts = $100 + $10x
The revenue from selling x shirts is:
$15 per shirt x x shirts = $15x
To break even:
$100 + $10x = $15x
Simplifying the equation:
$100 = $5x
x = 20
Therefore, the team needs to sell 20 shirts to break even.
were are the real people
Well, the team needs to cover the cost of printing design and setup, which is $100. Then, for each shirt, it costs them an additional $10. Since they will sell each shirt for $15, that means they'll make a profit of $5 per shirt sold.
To break even, they need to make enough profit to cover the initial cost. In this case, the total cost for the printing design and setup plus the number of shirts sold needs to equal the total revenue.
Let's denote the number of shirts they need to sell as "x".
The equation for this would be:
100 + 10x = 15x
Now, let's solve it!
Subtract 10x from both sides:
100 = 5x
Divide both sides by 5:
x = 100/5
x = 20
So, the team needs to sell 20 shirts in order to break even.
To break even, the total revenue needs to equal the total cost. Let's calculate the total cost first.
The cost for the printing design and setup is $100.
The cost per shirt is $10.
So, the total cost can be calculated as:
Total Cost = Printing Design and Setup Cost + (Cost per Shirt * Number of Shirts)
Now, let's calculate the total revenue.
The selling price per shirt is $15.
So, the total revenue can be calculated as:
Total Revenue = Selling Price per Shirt * Number of Shirts
To break even, Total Revenue = Total Cost.
Therefore,
Selling Price per Shirt * Number of Shirts = Printing Design and Setup Cost + (Cost per Shirt * Number of Shirts)
Simplifying the equation, we get:
15 * Number of Shirts = 100 + (10 * Number of Shirts)
Combining like terms, we have:
15 * Number of Shirts = 100 + 10 * Number of Shirts
Subtracting 10 * Number of Shirts from both sides, we get:
5 * Number of Shirts = 100
Now, divide both sides by 5 to solve for Number of Shirts:
Number of Shirts = 100 / 5
Therefore, the Lakewood baseball team needs to sell 20 shirts to break even.
To find out how many shirts the team needs to sell to break even, we need to calculate the total cost and the total revenue.
The total cost consists of two parts: the cost of printing design and setup ($100) and the cost per shirt ($10).
The total cost can be calculated using the formula:
Total Cost = Printing Design and Setup Cost + (Cost per Shirt × Number of Shirts)
Let's assume the team needs to sell x number of shirts to break even. Substituting the values into the formula, we get:
Total Cost = $100 + ($10 × x)
The total revenue is obtained by multiplying the selling price per shirt ($15) by the number of shirts sold, x.
Total Revenue = Selling Price per Shirt × Number of Shirts
Total Revenue = $15 × x
To break even, the total revenue needs to equal the total cost. Therefore, we can set up the following equation:
Selling Price per Shirt × Number of Shirts = Printing Design and Setup Cost + (Cost per Shirt × Number of Shirts)
Substituting the values, we have:
$15 × x = $100 + ($10 × x)
To solve for x, we can simplify the equation:
15x = 100 + 10x
5x = 100
x = 100 / 5
x = 20
Therefore, the team needs to sell 20 shirts to break even.