If winnie has a salary of 5,000 per week and has 10% on sales on x. Carmen has a salary of 4,500 and has a 15% sales on x.     Write the  linear functions

To model the salary of Winnie and Carmen as linear functions of their sales, denoted as $x$, we can set up the following functions:

1. **Winnie's Salary Function:**
   \[
   W(x) = 5000 + 0.10x
   \]
   - **Explanation**: Winnie has a base salary of 5,000 per week and earns an additional 10% on her sales, represented by $0.10x$.

2. **Carmen's Salary Function:**
   \[
   C(x) = 4500 + 0.15x
   \]
   - **Explanation**: Carmen has a base salary of 4,500 per week and earns an additional 15% on her sales, represented by $0.15x$.

These functions $W(x)$ and $C(x)$ represent the total weekly salaries of Winnie and Carmen, respectively, as functions of their sales $x$.

Would you like further details or have any questions?

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Here are five related questions to explore this concept further:

1. What would be Winnie's salary if her sales for the week were $2,000?
2. At what sales value $x$ would Winnie and Carmen have the same salary?
3. How much more would Carmen need to sell than Winnie to make up for her lower base salary?
4. If Winnie's sales double, how does her total salary change?
5. What is the percentage increase in Carmen's total salary if her sales increase by $1,000?

**Tip**: When comparing two linear functions, setting them equal and solving for the variable can help you find the point where the two functions intersect or when the salaries are the same.

Explore how to model Winnie and Carmen's weekly salaries using linear functions based on their base salaries and sales percentages. Includes examples and solutions for calculating salaries based on sales values. Suitable for Grades 7-9.

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