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Chapter 7: Problem 28

A salesperson receives a weekly salary of \(\$ 100,\) plus a \(5.5 \%\) commission on sales. Her salary last week was \(\$ 1090 .\) What were her sales that week?

Short Answer

Expert verified
The sales last week were \( \$ 18000 \).

Step by step solution

01

- Define Variables

Let the amount of sales last week be denoted as \( S \).
02

- Formulate the Salary Equation

The total salary last week is the sum of the base salary and the commission from sales. The equation is given by \( 1090 = 100 + 0.055S \).
03

- Simplify the Equation

Subtract the base salary from both sides to isolate the commission part: \( 1090 - 100 = 0.055S \). This simplifies to \( 990 = 0.055S \).
04

- Solve for Sales \( S \)

Divide both sides of the equation by the commission rate to find \( S \): \( S = \frac{990}{0.055} \).
05

- Calculate the Value of Sales

Perform the division: \( S = \frac{990}{0.055} = 18000 \). Therefore, the sales last week were \( \$ 18000 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Commission Calculations
Understanding commission calculations is vital for tackling problems like this one. A commission refers to the percentage of sales that a salesperson earns as part of their income. In this case, the saleswoman earns a 5.5% commission on her sales. To calculate the commission, you multiply the total sales amount by the commission rate. For example, if her total sales were \(S\) for the week, then her commission would be \((0.055 \times S)\). This commission is then added to her base salary to get the total income.
Variable Definition
Before solving any algebraic problem, it's important to define your variables clearly. In this exercise, we denote the total sales amount for the week as \(S\). This helps us set up an equation that can be solved step-by-step. **Tip:** Always specify what your variable represents to keep track of your calculations and avoid confusion.
Solving Linear Equations
Linear equations come in the form of \(ax + b = c\). Here, we reformulate the saleswoman's salary equation in a similar style: \(1090 = 100 + 0.055S\). To solve this equation, you need to isolate the variable \(S\). First, subtract the base salary \$100\ from both sides, then divide by the commission rate \0.055\. \ \begin{align*} 1090 - 100 &= 0.055S \ 990 &= 0.055S \ S &= \frac{990}{0.055} = 18000 \ \text{Therefore, her sales last week were} \ $18000 \end{align*}.
Basic Algebra
Basic algebra involves performing operations to solve for unknowns. **Key Steps:**
  • Identifying and defining the variables
  • Setting up an equation based on the given conditions
  • Simplifying the equation by performing opposite operations
  • Solving for the variable
  • Double-checking your solution
Remember:
Paying attention to arithmetic operations and correctly applying algebraic rules makes solving such exercises much easier.

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Most popular questions from this chapter

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