https://file.aiquickdraw.com/mathbot/file/1726776848631chz17zs4.jpg

Let's break down the problem to find the correct system of inequalities:

### Problem Recap:
Olivia works two part-time jobs: as a math tutor (with hours represented by \( t \)) and at a grocery store (with hours represented by \( s \)).

**Key conditions:**
1. Olivia works **no fewer than 20 total hours** at both jobs combined. This gives the inequality:
   \[
   t + s \geq 20
   \]
2. Olivia always spends **at least 5 more hours working as a math tutor** than she does at the grocery store. This translates to:
   \[
   t \geq s + 5
   \]

Now, let’s check the answer choices:

- **A.** \( t + s \geq 20 \), \( t \geq s + 5 \)
- **B.** \( t + s \geq 20 \), \( s \geq t + 5 \)
- **C.** \( t + s \leq 20 \), \( s \geq t + 5 \)
- **D.** \( t + s \leq 20 \), \( t \geq s + 5 \)

### Solution:
- The total hours are at least 20, so \( t + s \geq 20 \), ruling out options C and D (which have \( t + s \leq 20 \)).
- Olivia spends at least 5 more hours tutoring, so \( t \geq s + 5 \), ruling out option B (which incorrectly has \( s \geq t + 5 \)).

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

Would you like more details or have any other questions?

### Follow-up Questions:
1. How do you represent inequalities in real-world situations?
2. What is the difference between "at least" and "no more than" in inequalities?
3. How would the inequalities change if Olivia worked fewer than 20 total hours?
4. Can you represent this system of inequalities graphically?
5. What are other examples of systems of inequalities in real life?

**Tip:** Always pay attention to key phrases like "at least" or "no more than" when dealing with inequalities!

Olivia works two part-time jobs. Each week Olivia works no fewer than 20 total hours at the two jobs, and she always spends at least 5 more hours working as a math tutor than she spends working at the grocery store. Which system of inequalities represents the number of working hours, t, as a math tutor and the number of working hours, s, at the grocery store?

Explore how to solve a system of inequalities representing Olivia's working hours as a math tutor and at the grocery store. This problem covers key algebraic concepts, including systems of inequalities and their real-world application. Suitable for students in Grades 8-10.

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