Systems of Linear Equations Unit Test

Question

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Question
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?(1 point)
shirts

Answer 1

To determine how many shirts the Lakewood baseball team needs to sell to break even, we can set up an equation based on their costs and revenue.

Costs:

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

Total cost \( C \) for \( x \) shirts can be calculated as: \[ C = 100 + 10x \]

Revenue:

• Selling price per shirt: $15

Total revenue \( R \) from selling \( x \) shirts is: \[ R = 15x \]

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

Now, we'll solve for \( x \):

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

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

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