Jill is a writing tutor at her local community center. She has spent $400 on advertisements, and she pays the community center $20 per hour to use its facilities. She charges her clients $60 per hour.

Let's break down the financial details of Jill's tutoring business to understand her costs and earnings:

### Fixed Costs:
- **Advertisements**: Jill has spent a total of $400 on advertisements. This is a one-time, **fixed cost**.

### Variable Costs:
- **Hourly Facility Fee**: Jill pays the community center $20 per hour to use its facilities. This is a **variable cost** because it depends on the number of hours she tutors.

### Revenue:
- **Hourly Charge to Clients**: Jill charges her clients $60 per hour for her tutoring services.

### Profit Calculation:

To determine Jill's profit, we need to consider both her costs and her revenue.

1. **Total Costs**:
   - Fixed Costs (Advertisements): $400
   - Variable Costs (Hourly Facility Fee): $20 per hour

2. **Total Revenue**:
   - Revenue per hour: $60 per hour

3. **Profit per Hour**:
   - **Net Earnings per Hour**: Revenue per hour - Variable Costs per hour  
     $ = 60 - 20 = 40 $ dollars per hour

4. **Break-even Point**:
   - To find the break-even point (the number of hours Jill needs to tutor to cover all her costs), we set her total costs equal to her total revenue.

   Let's denote the number of hours Jill tutors by $ h $.

   \[
   \text{Total Costs} = \text{Fixed Costs} + \text{Variable Costs} \times h = 400 + 20h
   \]
   \[
   \text{Total Revenue} = \text{Revenue per hour} \times h = 60h
   \]

   Set Total Costs equal to Total Revenue:

   \[
   400 + 20h = 60h
   \]

   Solving for $ h $:

   \[
   400 = 60h - 20h
   \]
   \[
   400 = 40h
   \]
   \[
   h = \frac{400}{40} = 10
   \]

   Jill needs to tutor for **10 hours** to break even, covering both her fixed and variable costs. After this point, she will begin to make a profit.

### Summary:
- **Break-even Point**: 10 hours of tutoring.
- **Profit per hour after break-even**: $40 per hour.

Would you like to know more details or have any questions?

### Related Questions:

1. What would happen if Jill increased her hourly rate to $70?
2. How many hours does Jill need to tutor to make a $500 profit?
3. If Jill wants to spend $100 more on advertisements, how does that affect her break-even point?
4. How would a change in the community center's fee to $30 per hour affect Jill's break-even point?
5. What is the total profit if Jill tutors for 20 hours?

### Tip:
When running a small business, understanding both fixed and variable costs is crucial to determining profitability and making informed pricing decisions.

Understand Jill's tutoring business finances with a detailed breakdown of costs, revenue, and profit. Learn about fixed costs, variable costs, break-even point, and profit per hour calculations. Explore scenarios like increasing hourly rates and additional advertisement costs.

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