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.