You decide to market your own custom computer software. YOu must invest $3255 for computer hardware, and spend $2.90 to buy and package each disk. if each program sells for 13.75, how many copies must you drll to break even.

To determine how many copies of your software you need to sell to break even, we can use the following steps.

### Step 1: Define the variables.
- **Fixed cost** (hardware investment): $3255
- **Variable cost per disk** (cost to buy and package): $2.90
- **Selling price per program**: $13.75

### Step 2: Set up the break-even equation.
At the break-even point, the total revenue equals the total cost. The total cost includes both fixed and variable costs.

Let **x** be the number of copies you need to sell to break even.

The **total cost** is the sum of the fixed cost and the variable costs:
\[
\text{Total cost} = 3255 + 2.90x
\]

The **total revenue** is the selling price times the number of copies sold:
\[
\text{Total revenue} = 13.75x
\]

At the break-even point:
\[
\text{Total revenue} = \text{Total cost}
\]
So the equation is:
\[
13.75x = 3255 + 2.90x
\]

### Step 3: Solve for x.
First, subtract $2.90x$ from both sides to isolate $x$ on one side:
\[
13.75x - 2.90x = 3255
\]
\[
10.85x = 3255
\]

Now, divide both sides by 10.85 to solve for $x$:
\[
x = \frac{3255}{10.85} \approx 300
\]

### Conclusion:
You need to sell approximately **300 copies** of the software to break even.

---

Would you like more details on this process or any clarification? Here are 5 related questions:

1. How would the break-even point change if the selling price increased?
2. What happens to the break-even point if the cost of hardware increases?
3. How does a higher variable cost per disk affect the number of sales needed to break even?
4. If you offered a discount, how would it impact the break-even point?
5. How would selling through a digital platform (with no packaging cost) affect the analysis?

**Tip:** When planning a business, always consider both fixed and variable costs to understand the true break-even point effectively.

You decide to market your own custom computer software. You must invest $3255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how many copies must you sell to break even?

Learn how to calculate the break-even point for selling custom computer software, considering hardware investment and variable packaging costs. Understand the algebraic approach to solving for the number of sales required to cover both fixed and variable costs. Suitable for Grades 9-11.

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