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)

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

GPT-4o mini · Answer

To determine how many shirts the Lakewood baseball team needs to sell to break even, we first need to calculate the total cost and the total revenue.

Total Cost: The total cost consists of the fixed cost for printing and the variable cost per shirt:

Fixed cost: $100 (design and setup)
Variable cost per shirt: $10

If $ x $ is the number of shirts sold, then the total cost (TC) can be calculated as: \[ \text{Total Cost} = 100 + 10x \]

Total Revenue: The total revenue is generated from selling the shirts at $15 each. Therefore, the total revenue (TR) is: \[ \text{Total Revenue} = 15x \]

Break-even Point: To find the break-even point, we set total cost equal to total revenue: \[ 100 + 10x = 15x \]

Now, we can solve for $ x $:

Subtract $ 10x $ from both sides: \[ 100 = 15x - 10x \] \[ 100 = 5x \]
Now divide both sides by 5: \[ x = \frac{100}{5} = 20 \]

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