Juliet has a choice between receiving a monthly salary of ​$1800 from a company or a base salary of ​$1400 and a 5​% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be​ equal?

To find the amount of sales where Juliet's two salary choices are equal, let's define:

- $ S $ as the amount of furniture she sells in a month.
- The first option is a fixed salary of $1800 per month.
- The second option is a base salary of $1400 plus a 5% commission on sales, which is $ 0.05S $.

We want to find the sales amount $ S $ where these two options give the same salary.

### Step-by-step solution:

1. **Fixed salary equation:**
   \[
   1800
   \]

2. **Commission salary equation:**
   \[
   1400 + 0.05S
   \]

3. **Set the two salary options equal to each other:**
   \[
   1800 = 1400 + 0.05S
   \]

4. **Solve for $ S $:**

   Subtract 1400 from both sides:
   \[
   1800 - 1400 = 0.05S
   \]
   \[
   400 = 0.05S
   \]

   Divide both sides by 0.05:
   \[
   S = \frac{400}{0.05} = 8000
   \]

Thus, the amount of sales at which the two salary options are equal is **$8000**.

Would you like more details or have any questions? Here are some related questions to explore:

1. What if the commission rate changes to 7%?
2. How much would she earn with the commission if her sales were $9000?
3. At what sales level would the commission-based salary exceed the fixed salary?
4. What happens if the base salary in the commission plan decreases to $1300?
5. How does increasing the fixed salary affect the equality point?

**Tip:** Always check commission rates and base salaries in job offers to calculate the breakeven point between fixed and commission-based options.

Juliet has a choice between receiving a monthly salary of $1800 from a company or a base salary of $1400 and a 5% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be equal?

Discover how to calculate the sales amount at which a fixed salary of $1800 equals a base salary of $1400 plus a 5% commission. This step-by-step guide walks you through solving the linear equation to find the breakeven point, suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation