To date, this year, Company XYZ has sold 525 units. They sell units at an average rate of 15 per week. The company wants to sell more than 750 units this year. Which of the following inequalities could be used to solve for *x*, the number of weeks necessary to reach the company's year-end goal?

 **A.** 

15*x* - 525 > 750

 **B.** 

15*x* > 750

 **C.** 

15*x* + 525 > 750

 **D.** 

15*x* > 1,275

To determine which inequality can be used to solve for *x*, the number of weeks necessary to reach the company's year-end goal, let's break down the problem.

### Information Given:
- Company XYZ has already sold 525 units.
- The company sells units at an average rate of 15 per week.
- The company wants to sell more than 750 units this year.

### Problem Breakdown:
Let *x* represent the number of weeks necessary to reach the company's year-end goal.

1. The company has already sold 525 units. 
2. In *x* weeks, they will sell an additional \(15 \times x\) units.
3. The total number of units sold after *x* weeks will be:
   \[
   525 + 15x
   \]
4. The company wants this total to be more than 750 units:
   \[
   525 + 15x > 750
   \]
   
5. Now, solve the inequality:
   \[
   15x > 750 - 525
   \]
   \[
   15x > 225
   \]
   \[
   x > \frac{225}{15}
   \]
   \[
   x > 15
   \]

This inequality shows that the company needs more than 15 weeks to reach their goal of selling more than 750 units this year.

### Conclusion:
The correct inequality to use is:

**C.** \(15x + 525 > 750\)

Do you want further details or have any questions?

### Related Questions:
1. How many weeks will it take for the company to reach exactly 750 units sold?
2. If the company sells 20 units per week, how would the inequality change?
3. What if the company had already sold 600 units? How would this affect the inequality?
4. How many units will the company have sold after 20 weeks?
5. What is the minimum number of weeks needed to reach 1,000 units sold?
6. How would a change in the weekly sales rate to 10 units per week affect the solution?
7. What if the goal was to sell 1,000 units instead of 750?
8. What is the inequality if the goal is to sell at least 750 units?

### Tip:
When dealing with inequalities involving word problems, carefully translate the words into mathematical expressions, ensuring all quantities and conditions are accounted for.

Learn how to solve the inequality to determine the number of weeks necessary for Company XYZ to reach their year-end sales goal. This problem involves applying inequalities and linear equations to real-world sales scenarios. Suitable for high school students.

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