Juliet has a choice between receiving a monthly salary of ​$1620 from a company or a base salary of ​$1300 and a 4​% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be​ equal?

Let $ x $ represent the amount of furniture sales Juliet makes in a month.

### Option 1:
She receives a fixed salary of $ 1620 $ dollars.

### Option 2:
She receives a base salary of $ 1300 $ dollars plus a 4% commission on sales, i.e., $ 0.04x $.

The total salary for this option is:  
\[
\text{Salary} = 1300 + 0.04x
\]

### Setting the two options equal:
\[
1620 = 1300 + 0.04x
\]

Now, solve for $ x $:

1. Subtract $ 1300 $ from both sides:
\[
1620 - 1300 = 0.04x
\]
\[
320 = 0.04x
\]

2. Divide both sides by $ 0.04 $:
\[
x = \frac{320}{0.04} = 8000
\]

Thus, the two salary options will be equal when her sales amount to **$8,000**.

Would you like further details, or do you have any questions?

---

Here are 5 related questions for further practice:
1. What would her salary be if she sold $10,000 worth of furniture?
2. What is the commission if she sells $5,000 worth of furniture?
3. How much should she sell to make more than $2,000 in total salary?
4. If the commission increased to 5%, how would the breakeven sales change?
5. How much does she earn if she sells no furniture?

**Tip:** Break-even points occur when two options produce the same result, and they can be found by setting the options equal and solving for the unknown.

Juliet has a choice between receiving a monthly salary of $1620 from a company or a base salary of $1300 and a 4% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be equal?

Learn how to find the break-even point between a fixed salary of $1620 and a commission-based salary with a base of $1300 and a 4% commission. This algebra problem teaches how to set up and solve a linear equation. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation