The school incurs a loss of $1.5 per T-shirt when selling 20 shirts and makes a profit of $6.5 per T-shirt when selling 100 shirts. To break even, they need to sell 4 shirts.
The school's T-shirt fundraising campaign involves analyzing the financial outcomes based on the quantity of shirts sold. When 20 shirts are sold, the school incurs a loss of $30. Conversely, selling 100 shirts results in a profit of $650.
To determine the profit or loss per T-shirt, we can calculate the unit profit or loss by dividing the total financial outcome by the respective quantity of shirts. For the loss scenario:
Loss per T-shirt = Total Loss / Number of Shirts = -30 / 20 = -$1.5 per T-shirt
For the profit scenario:
Profit per T-shirt = Total Profit / Number of Shirts = $650 / 100 = $6.5 per T-shirt
Therefore, the school incurs a loss of $1.5 per T-shirt when selling 20 shirts but makes a profit of $6.5 per T-shirt when selling 100 shirts.
To find the quantity of shirts needed to break even, we set the total profit equal to the total loss:
Total Loss = Total Profit
-30 + Number of Shirts to Break Even * Loss per T-shirt = Number of Shirts to Break Even * Profit per T-shirt
Solving for the number of shirts to break even:
-30 + Number of Shirts to Break Even * (-1.5) = Number of Shirts to Break Even * 6.5
6.5 * Number of Shirts to Break Even + 1.5 * Number of Shirts to Break Even = 30
8 * Number of Shirts to Break Even = 30
Number of Shirts to Break Even = 30 / 8 = 3.75
Since the number of shirts must be a whole number, the school needs to sell 4 shirts to break even.
The question probable may be:
A school is organizing a T-shirt fundraising campaign. If they sell 20 shirts, they incur a loss of $30. However, by selling 100 shirts, they generate a profit of $650. Determine the school's profit or loss per T-shirt and find the quantity of shirts they need to sell to break even.