Given the following notations, write a formula for x, the break-even sales level.
SP = selling price per unit
FC = total fixed cost
VC = variable cost per unit

The break-even sales level \( x \) is the point at which total revenue equals total costs (both fixed and variable costs). The formula for the break-even sales level is derived by setting the total revenue equal to the total costs.

Here’s how to set it up:

- **Revenue** is the selling price per unit (\( SP \)) multiplied by the number of units sold (\( x \)).
  \[
  \text{Revenue} = SP \times x
  \]
  
- **Total cost** is the sum of the fixed cost (\( FC \)) and the variable cost per unit (\( VC \)) multiplied by the number of units sold (\( x \)).
  \[
  \text{Total cost} = FC + VC \times x
  \]

To find the break-even sales level \( x \), set the total revenue equal to the total cost:
\[
SP \times x = FC + VC \times x
\]

Now, solve for \( x \):

1. Subtract \( VC \times x \) from both sides:
   \[
   SP \times x - VC \times x = FC
   \]
   
2. Factor out \( x \) on the left side:
   \[
   x(SP - VC) = FC
   \]
   
3. Solve for \( x \):
   \[
   x = \frac{FC}{SP - VC}
   \]

So, the formula for the break-even sales level is:
\[
x = \frac{FC}{SP - VC}
\]

### Do you need more details or further clarification?

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Here are 5 related questions to further explore this concept:

1. How do changes in the selling price affect the break-even point?
2. What happens to the break-even sales level if the variable cost per unit increases?
3. How would the formula change if there were multiple products with different selling prices and variable costs?
4. What is the impact of reducing fixed costs on the break-even sales level?
5. How can the break-even analysis be used for decision-making in pricing strategies?

**Tip:** Always compare the selling price to the variable cost when determining profitability—higher margins lower the break-even point.

Given the following notations, write a formula for x, the break-even sales level. SP = selling price per unit, FC = total fixed cost, VC = variable cost per unit.

Learn how to calculate the break-even sales level using the formula x = FC / (SP - VC). This problem covers key algebraic concepts and break-even analysis, suitable for students in Grades 9-12. Understand how fixed and variable costs impact the break-even point.

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