The lakewood baseball team is selling t-shirts for a fundraiser. the shirts cost $100 for the printing design the setup, plus $10 per shirt. the team is going to sell the shirts for $15 each. how many shirts do they need to break even?

1 answer

To determine how many t-shirts the Lakewood baseball team needs to sell to break even, we first need to calculate the total costs and revenues.

Costs:

  • Fixed cost for printing and setup: $100
  • Variable cost per shirt: $10

Let \( x \) be the number of shirts sold. The total cost can be calculated as: \[ \text{Total Cost} = 100 + 10x \]

Revenues:

  • Selling price per shirt: $15
  • Total revenue from selling \( x \) shirts: \[ \text{Total Revenue} = 15x \]

Break-even point: To break even, the total revenue must equal the total cost: \[ 15x = 100 + 10x \]

Now, we can solve for \( x \):

  1. Subtract \( 10x \) from both sides: \[ 15x - 10x = 100 \] \[ 5x = 100 \]

  2. Divide by 5: \[ x = \frac{100}{5} = 20 \]

Therefore, the team needs to sell 20 shirts to break even.