Question

Perry's Used Cars gives \(\frac{1}{8}\) of the price of a car as commission to its sales force. The members of the sales force share equally in the commission. If there are 6 people selling cars, how much will each get from a car that sells for \(\$ 7100\) ? Write your answer in the box.

Short answer

Each member receives $147.92.

Step-by-step solution

Calculate Total Commission

To find the total commission given by Perry's Used Cars, multiply the price of the car by the commission rate: \[ \text{Total Commission} = \frac{1}{8} \times 7100 \] Calculate the product to find the total commission.

Solve for Total Commission

Perform the multiplication: \[ \text{Total Commission} = \frac{1}{8} \times 7100 = 887.50 \] Therefore, the total commission on a car that sells for \(7100 is \)887.50.

Distribute the Commission Equally

Since there are 6 people in the sales force, divide the total commission by 6 to find out how much each person gets: \[ \text{Commission per person} = \frac{887.50}{6} \] Perform the division to find the commission per person.

Solve for Individual Commission

Perform the division: \[ \text{Commission per person} = \frac{887.50}{6} \ \text{Commission per person} \ \text{Commission per person} = 147.92 \] Thus, each member of the sales force receives \(147.92 from selling the car for \)7100.

Key concepts

Division of Amounts

Division of amounts is a basic arithmetic operation where a total amount is distributed into equal parts. In this exercise, we need to divide the total commission by the number of salespeople.
First, determine the total commission: \[ \text{Total Commission} = \frac{887.50}{6} \] Then, divide this amount equally among the 6 sales force members.
It's important to always ensure the division is done accurately to get the correct share for each person.

Fraction Multiplication

Fraction multiplication is a way to find a part of an amount. In this example, \[ \text{Commission} = \frac{1}{8} \times 7100 \]
Here, \( \frac{1}{8} \) means taking one part out of eight parts of the total price of the car. This step is essential because it tells us how much commission is earned off the total sale price.
The multiplication of the fraction and the sale price is performed to calculate the total commission for the car sale.

Equal Sharing

Equal sharing ensures that each member of a group receives an identical portion of the total. In the context of this exercise, after calculating the total commission, we share this equally among the 6 salespeople.
Calculate as: \[ \text{Commission per person} = \frac{887.50}{6} \] Each individual gets the same amount, ensuring fair distribution. Equal sharing is a foundation of fairness in any collective effort or reward system.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations are fundamental in solving most mathematical problems.
In this example:

• Multiplication: to calculate the total commission.
• Division: to distribute the commission equally among the salespeople.

Understanding and performing these operations accurately is crucial for problem-solving and ensuring correct results.