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

Question

How many shirts do they need to sell to break even?

Answer 1

To determine how many shirts the Lakewood baseball team needs to sell to break even, we need to set up the costs and revenue equations.

1. Cost Equation:

   • Fixed cost (printing design and setup): $100
   • Variable cost per shirt: $10
   • If \( x \) is the number of shirts sold, then the total cost \( C \) can be expressed as: \[ C = 100 + 10x \]

2. Revenue Equation:

   • Selling price per shirt: $15
   • The total revenue \( R \) from selling \( x \) shirts is: \[ R = 15x \]

3. Break-Even Point: At the break-even point, the total revenue equals total cost: \[ R = C \] Substituting the equations we have: \[ 15x = 100 + 10x \]

4. Solving for \( x \):

   • Rearranging the equation: \[ 15x - 10x = 100 \] \[ 5x = 100 \] \[ x = \frac{100}{5} = 20 \]

The Lakewood baseball team needs to sell 20 shirts to break even.