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 \( x \):
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Subtract \( 10x \) from both sides: \[ 15x - 10x = 100 \] \[ 5x = 100 \]
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Divide by 5: \[ x = \frac{100}{5} = 20 \]
Therefore, the team needs to sell 20 shirts to break even.