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The question is about two roommates, Grace and Frances, and their respective earnings from work. Here’s how to address the problem:

### a. Domain and Range of the Function for Frances' Pay
The function for Frances’ pay is given by $ f(t) = 10t $, where $ t $ is the number of hours Frances works per week and is restricted to $ 5 \leq t \leq 15 $.

- **Domain**: The domain represents the possible values of $ t $ (hours worked by Frances). Since the problem specifies that $ t $ is between 5 and 15 hours, the domain is:
  \[
  \text{Domain} = [5, 15]
  \]
- **Range**: The range represents the possible values of $ f(t) $ (Frances' pay). To find the range, evaluate the function at the endpoints of the domain:
  \[
  f(5) = 10(5) = 50, \quad f(15) = 10(15) = 150
  \]
  Therefore, the range is:
  \[
  \text{Range} = [50, 150]
  \]

### b. Comparison of Hourly Wages and Weekly Earnings
- **Grace's Hourly Wage**: Grace earns $9.00 per hour.
- **Frances's Hourly Wage**: Frances earns $10.00 per hour (since $ f(t) = 10t $, the coefficient of $ t $ represents her hourly wage).

#### Weekly Earnings
- **Grace's Weekly Earnings**: Grace works between 10 and 20 hours, so her weekly earnings range between:
  \[
  9(10) = 90 \quad \text{and} \quad 9(20) = 180
  \]
  Thus, Grace's weekly earnings are between $90 and $180.
  
- **Frances's Weekly Earnings**: From the range of Frances’ pay, we know her weekly earnings are between $50 and $150 (as calculated in part a).

### Summary:
- Grace earns $9.00 per hour and her weekly earnings range from $90 to $180.
- Frances earns $10.00 per hour and her weekly earnings range from $50 to $150.

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Do you want more detailed explanations or have any further questions?

Here are 5 related questions you might find helpful:
1. How would Frances' weekly pay change if she worked more than 15 hours?
2. What would happen if Grace's hourly wage increased to $10.50 per hour?
3. How would you calculate Grace's total earnings over a semester if she worked 15 hours per week for 12 weeks?
4. What is the average weekly pay for Frances if she works the maximum number of hours (15)?
5. If Frances wanted to earn as much as Grace's maximum weekly earnings, how many hours would she need to work at her current wage?

**Tip**: Always pay attention to units (hours, dollars, etc.) when comparing or calculating wages!

Grace works from 10 to 20 hours per week while attending college. She earns $9.00 per hour. Her roommate Frances also has a job. Her pay for t hours each week is given by the function f(t) = 10t, where 5 ≤ t ≤ 15.

Solve a problem involving the weekly earnings of two college roommates. Grace earns $9 per hour working 10 to 20 hours per week, while Frances' pay is given by the function f(t) = 10t, where 5 ≤ t ≤ 15. Learn to find the domain and range of the function and compare their wages.

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