https://file.aiquickdraw.com/mathbot/file/1730217733572u29b3ugi.jpg

To solve this problem, let's break down each part of the question.

### Step 1: Understanding the Variables
Let:
- $ x $ = hours Jeremy works babysitting (at $7.25 per hour).
- $ y $ = hours Jeremy works as a library assistant (at $14.50 per hour, which is twice as much as babysitting).

### Step 2: Analyzing the Conditions
1. **Total Weekly Hours**: Jeremy can work a maximum of 20 hours per week. This gives the inequality:
   \[
   x + y \leq 20
   \]

2. **Income Goal**: Jeremy wants to earn more than $100 per week. The total earnings are given by:
   \[
   7.25x + 14.50y > 100
   \]

### Step 3: Identifying the Correct Inequalities
The correct system of inequalities that represents these conditions is:
\[
\begin{cases}
x + y \leq 20 \\
7.25x + 14.50y > 100
\end{cases}
\]

### Step 4: Matching with the Options
From the options given:
- **Option D** correctly represents the system of inequalities:
  \[
  x + y \leq 20 \quad \text{and} \quad 7.25x + 14.50y > 100
  \]

### Final Answer
The correct answer is **D**.

Would you like further details or explanations on any part of this solution?

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Here are five related questions to deepen understanding:
1. What would the inequalities look like if Jeremy could work up to 25 hours instead of 20?
2. How would the inequalities change if the library assistant job paid $10 per hour instead?
3. If Jeremy wanted to earn at least $150 per week, how would the inequality change?
4. How can this system of inequalities be graphed on a coordinate plane?
5. How many hours should Jeremy work in each job to maximize his income under these constraints?

**Tip:** When setting up inequalities, carefully analyze each condition separately before combining them into a system.

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?

Solve a linear inequalities system where Jeremy works as a babysitter at $7.25 per hour and a library assistant earning twice as much per hour. He needs to make over $100 per week but can work up to 20 hours. Learn how to determine the possible combinations of hours worked in each job.

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