Jeremy has a babysitting job after school that pays $7.25 per hour. He earns twice as much per hour working as a library assistant. He wants to make more than $100 a week, but work at most 20 hours per week.

Which system of linear inequalities represents all possible combinations of the number of hours babysitting, x, and the number of hours as a library assistant, y, Jeremy can work?
A.x + y < 20
7.25x + 15y > 100
B.x + y < 20
7.25x + 14.50y > 100
C.x + y ≥ 20
7.25x + 15y ≥ 100
D.x + y ≤ 20
7.25x + 14.50y > 100


To represent the situation with a system of linear inequalities, let's break down the requirements:

1. **Total hours constraint**: Jeremy can work at most 20 hours a week.
   - This gives us the inequality: $ x + y \leq 20 $

2. **Earnings constraint**: He wants to make more than $100 a week.
   - Jeremy earns $7.25 per hour babysitting and $14.50 per hour as a library assistant (since he earns twice as much as his babysitting rate).
   - This gives us the inequality: $ 7.25x + 14.50y > 100 $

Now, matching these inequalities to the options provided:

- **Option D** is: 
   - $ x + y \leq 20 $
   - $ 7.25x + 14.50y > 100 $

Therefore, the correct answer is **D**.

### Summary of System of Inequalities
1. $ x + y \leq 20 $ (total hours)
2. $ 7.25x + 14.50y > 100 $ (earnings)

Would you like more details on how to solve this or have any questions about the setup? Here are some related questions:

1. What is the maximum amount Jeremy can earn if he works 20 hours?
2. How many hours can he work as a library assistant if he babysits for a certain number of hours?
3. What would be the total earnings if he worked exactly 10 hours as a babysitter?
4. Can you find the combinations of hours that meet both constraints?
5. What is the graphical representation of this system of inequalities? 

**Tip**: Always ensure to check the constraints to find feasible solutions in problems involving inequalities.

Jeremy has a babysitting job after school that pays $7.25 per hour. He earns twice as much per hour working as a library assistant. He wants to make more than $100 a week, but work at most 20 hours per week. Which system of linear inequalities represents all possible combinations of the number of hours babysitting, x, and the number of hours as a library assistant, y, Jeremy can work?

Explore the system of linear inequalities that defines Jeremy's work hours as a babysitter and library assistant. This problem illustrates how to set up inequalities based on hourly wages and work constraints, suitable for students in Grades 8-10.

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