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)
To break even, the total revenue from selling the shirts needs to equal the total cost of printing and setup.
Let's call the number of shirts the team needs to sell "x".
The cost of printing design and setup is a fixed cost of $100.
The cost per shirt is $10.
The selling price per shirt is $15.
The total cost is the sum of the fixed cost and the cost per shirt, multiplied by the number of shirts:
Total cost = $100 + ($10 * x)
The total revenue is the selling price per shirt multiplied by the number of shirts:
Total revenue = $15 * x
To break even, the total revenue must equal the total cost:
Total revenue = Total cost
$15 * x = $100 + ($10 * x)
Now, we can solve for x:
$15 * x - $10 * x = $100
$5 * x = $100
x = $100 / $5
x = 20
Therefore, the team needs to sell 20 shirts to break even.
To determine how many shirts the Lakewood baseball team needs to sell to break even, we need to consider the cost and revenue involved.
1. Start by calculating the total cost: The team incurs a fixed cost of $100 for the printing design and setup, plus a variable cost of $10 per shirt. So, the cost to produce each shirt is $100 + $10 = $110.
2. Next, determine the selling price per shirt: The team plans to sell each shirt for $15.
3. Calculate the profit or loss per shirt: The profit or loss per shirt is the selling price minus the cost per shirt. In this case, it is $15 - $110 = -$95.
4. To break even, the profit per shirt must be zero. Therefore, set up the equation $15 - $110 = 0 and solve for x, where x represents the number of shirts the team needs to sell.
$15x - $110x = 0
-$95x = 0
x = 0 / -$95
x = 0
Based on the calculation, the team needs to sell 0 shirts to break even. However, this result is not practically possible. It suggests that in order to cover the fixed cost of $100, they will need to sell additional shirts.
So, to determine the actual quantity of shirts they need to sell to cover the fixed cost, divide the fixed cost by the profit per shirt:
$100 / -$95 ≈ 1.05
Rounding up, the team needs to sell at least 2 shirts to break even.