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.