Final answer:
The student needs to create a system of equations to calculate the break-even point for selling computer software disks. They need to equate the total costs (fixed and variable) with the total revenue to determine the number of disks required to sell to cover all costs.
Step-by-step explanation:
The question seems to be based on creating a system of equations to determine how many disks you need to sell to break even when starting a business selling computer software. To calculate this, we must consider both the fixed and variable costs associated with producing the disks and compare them with the revenue earned per disk sold.
The initial investment in computer hardware is $3,255, which is a fixed cost. The variable cost includes the cost of buying a package for each disk, which is $2.90. Each disk sells for $13.75. To break even, the revenue from selling the disks must equal the total costs (fixed costs + variable costs).
Let's denote the number of disks needed to be sold to break even as x. The system of equations to represent the break-even analysis would be:
- Total cost = Fixed cost + (Variable cost per disk × Number of disks)
- Total revenue = Selling price per disk × Number of disks
Substituting the known values gives us the equations:
- Total cost = $3,255 + ($2.90 × x)
- Total revenue = $13.75 × x
To find the break-even point, we set the total cost equal to the total revenue:
$3,255 + ($2.90 × x) = $13.75 × x
This equation can then be solved to find the value of x, the number of disks that need to be sold to break even.