https://file.aiquickdraw.com/mathbot/file/1726114472604h7q89qtq.jpg

To solve the problem, we need to compare Annette’s earnings from both job offers as functions of the number of shoes she sells, then find the range of sales where one job offers a better total income than the other.

### Job offers:

1. **Comfort over Style Shoe Emporium:**
   - Fixed salary: $52,000
   - Additional earnings per pair of shoes sold: $3.25

   Total earnings equation:
   \[
   \text{Earnings from Comfort} = 52000 + 3.25x
   \]
   where $x$ is the number of shoes sold.

2. **Heels for Fashion Slaves Boutique:**
   - Fixed salary: $37,000
   - Additional earnings per pair of shoes sold: $4.75

   Total earnings equation:
   \[
   \text{Earnings from Heels} = 37000 + 4.75x
   \]

### Step 1: Set up the inequality
We need to find out when the total earnings from Comfort over Style are greater than the total earnings from Heels for Fashion Slaves. Therefore, the inequality is:
\[
52000 + 3.25x > 37000 + 4.75x
\]

### Step 2: Solve the inequality
First, subtract $37,000 from both sides:
\[
52000 - 37000 + 3.25x > 4.75x
\]
\[
15000 + 3.25x > 4.75x
\]

Next, subtract $3.25x$ from both sides:
\[
15000 > 1.5x
\]

Now, divide by 1.5:
\[
x < 10000
\]

### Conclusion:
Annette will make more from the Comfort over Style Shoe Emporium job if she sells fewer than 10,000 pairs of shoes.

Let me know if you'd like more details or if you have any questions!

### Follow-up questions:
1. How would the solution change if the fixed salaries were different?
2. What happens if the per-shoe earnings at both jobs were equal?
3. How does the rate of per-shoe sales affect the break-even point?
4. Can you create a graph to visualize the two job offers' earnings?
5. What if the $4.75 earnings from Heels Boutique decreased slightly—how would that impact the inequality?

### Tip:
Always remember to isolate the variable on one side to solve inequalities effectively!

Annette the shoe salesperson has two job offers. The Comfort over Style Shoe Emporium has offered her a $52,000 salary plus $3.25 for every pair of shoes she sells. The Heels for Fashion Slaves Boutique has offered a $37,000 salary plus $4.75 for every pair of shoes she sells. Over what range of shoe sales will Annette make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job?

Learn how to solve a real-world problem comparing two job offers with different salaries and per-shoe sales earnings. This problem covers key algebraic concepts such as linear inequalities and solving for unknowns, and is suitable for students in Grades 7-10.

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