Question

A school decides to sell t-shirts to raise money. if theynsell 20 shirts they will lose 30 dollars. If they sell 100 shirts they will make 650 dollars. how many shirts do they need to sell to break even?

Answer 1

By setting up a linear equation, we find the school must sell approximately 23.53 t-shirts to break even. Since the school cannot sell a fraction of a shirt, they would need to sell 24 t-shirts to reach the break-even point.

Step-by-step explanation:

To determine how many t-shirts need to be sold to break even, we need to set up a linear equation based on the information provided. We know that selling 20 shirts results in a loss of $30, and selling 100 shirts results in a profit of $650.

Let's define the number of shirts sold as 'x' and the total money gained or lost as 'y'. We have two points: (20, -30) and (100, 650). We can find the slope (m) of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values:

m = (650 - (-30)) / (100 - 20) = 680 / 80 = 8.5

This means the equation of the line can be written as:

y = 8.5x + b

Using the point (20, -30) to solve for 'b', we substitute 'x' and 'y' in the equation:

-30 = 8.5(20) + b

b = -30 - 170

b = -200

Thus, the equation of the line is:

y = 8.5x - 200

To find the break-even point where y = 0:

0 = 8.5x - 200

Solving for x:

x = 200 / 8.5

x ≈ 23.53

Since the school cannot sell a fraction of a shirt, they would need to sell 24 t-shirts to break even.