https://file.aiquickdraw.com/mathbot/file/1729038704097o5z3hlaq.jpg

Let's solve this step by step.

### Information from the problem:
- **Plan 1:**  
  $450 per week + 4% commission on sales  
  This means salary = $ 450 + 0.04 \times S $, where $ S $ is the amount of sales.

- **Plan 2:**  
  $150 per week + 18% commission on sales  
  This means salary = $ 150 + 0.18 \times S $.

### Goal:
We need to determine the amount of sales $ S $ such that both plans result in the **same weekly salary**. Therefore, we equate the two salary expressions:

\[
450 + 0.04 \times S = 150 + 0.18 \times S
\]

---

### Step 1: Rearrange the equation.
Move all terms involving $ S $ to one side and constant terms to the other:

\[
450 - 150 = 0.18 \times S - 0.04 \times S
\]

\[
300 = 0.14 \times S
\]

---

### Step 2: Solve for $ S $.

\[
S = \frac{300}{0.14} = 2142.86
\]

---

### Conclusion:
Becky needs to make **$2142.86** in sales for the salaries to be the same under both plans.

Let me know if you have any questions or need further clarification!

---

**Here are 5 related questions:**
1. What happens if Becky sells more than $2142.86? Which plan would be better?
2. How do the commissions change the break-even point if Plan 2's percentage is adjusted?
3. What is the total weekly salary for both plans if Becky makes $3000 in sales?
4. How would the break-even sales change if Plan 1 increased the base salary?
5. How can you determine which plan is better if Becky’s sales vary week to week?

**Tip:**  
When comparing two salary plans, always look for the point where they are equal. Beyond that point, one plan might offer higher returns!

Becky Schwartz, a saleswoman, is offered two salary plans. Plan 1 is $450 per week salary plus a 4% commission of sales. Plan 2 is a $150 per week salary plus an 18% commission of sales. How much would Becky need to make in sales for the salary to be the same from both plans?

Solve a sales commission problem where Becky needs to determine the amount of sales required to make her weekly salary the same under two different commission plans. This problem involves algebra and linear equations suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation