the startup cost for a restaurant is $120,000, and each meal costs $10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even?

To find the break-even point for the restaurant, we need to determine when the total revenue equals the total cost. 

### Step 1: Define the variables
- **Fixed costs (Startup costs):** $120,000
- **Cost per meal (Variable cost):** $10
- **Selling price per meal:** $15

### Step 2: Write the cost and revenue equations
- **Total Cost (C):** This includes both fixed costs and variable costs.  
  $ C = 120,000 + 10x $  
  where $ x $ is the number of meals sold.

- **Total Revenue (R):** This is the income from selling meals.  
  $ R = 15x $

### Step 3: Set the equations equal to find the break-even point
At the break-even point, Total Revenue equals Total Cost:
\[
15x = 120,000 + 10x
\]

### Step 4: Solve for $ x $
Subtract $ 10x $ from both sides:
\[
5x = 120,000
\]

Now, divide by 5:
\[
x = 24,000
\]

### Conclusion:
The restaurant needs to sell **24,000 meals** to break even.

Would you like more details on any part of the solution? Here are some related questions:

1. How much profit will the restaurant make if they sell 30,000 meals?
2. What would be the new break-even point if the selling price per meal increased to $20?
3. How would the break-even point change if the cost per meal decreased to $8?
4. What would happen to the break-even point if the startup cost increased to $150,000?
5. How long would it take to reach the break-even point if the restaurant sells 500 meals per day?

**Tip:** The break-even point is crucial for businesses to understand when they will start making a profit. It's important to consider both fixed and variable costs when calculating it.

Learn how to calculate the break-even point for a restaurant with a startup cost of $120,000. Understand the relationship between fixed costs, variable costs, selling price, and quantity sold. Find out how many meals the restaurant needs to sell to break even.

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