Commission

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Commission: meaning, method and solved example (7th Grade) – Maths PDF


In short: Commission is pay that a worker earns as a percent of the money from the goods or services they sell, so more sales mean a bigger paycheck.

7th GradeRatios and Percents7.RP.A.3

What is Commission?

A salesperson who earns a commission gets a cut of every sale instead of, or on top of, a fixed wage. The cut is a percent of the sales total, so the paycheck rises and falls with performance.

With total sales \(S\) and a rate \(r\) as a decimal, the pay from the percent is \(S \times r\). Some jobs add a base salary \(B\), giving total earnings \(B + S \times r\). Real estate agents, car dealers and furniture sellers are paid this way.

How to spot it

  • A job description says the worker earns a percent of what they sell, such as 6.5% of furniture sales.
  • A problem lists weekly sales totals and asks for the paycheck that results from them.
  • Earnings are split into a fixed base amount plus a variable part that depends on sales.
  • You are given the pay and the sales and asked for the percent rate the employer used.

The method

  1. Find the sales total the percent applies to, adding up several sales if needed.
  2. Convert the percent to a decimal and multiply it by the sales total.
  3. Add any base salary or bonus to that product to get the full earnings.
  4. To find the rate, divide the earned amount by the sales total and write the quotient as a percent.
Total earnings $950base $4504% of $12,500= $50012,500 × 0.04 = 500450 + 500 = 950
Base pay of $450 plus 4% of $12,500 in sales equals $950.

Commission: solved example

Problem

Nadia sells furniture and earns 6.5% on every sale. In March her sales total \(\$18{,}400\). How much commission does she earn?

Solution

Rate as a decimal: \(6.5\% = 0.065\).

Multiply: \(18{,}400 \times 0.065 = 1{,}196\). Nadia earns \(\$1{,}196\) for the month.

Try it

Question 1

A car salesperson has a base pay of \(\$600\) and earns 2% on \(\$31{,}000\) of sales. What are the total earnings?

Show the answer

\(31{,}000 \times 0.02 = 620\), then \(600 + 620 = 1{,}220\). Total: \(\$1{,}220\).

Question 2

An agent earned \(\$210\) on \(\$3{,}500\) of sales. What was the rate?

Show the answer

\(\frac{210}{3{,}500} = 0.06\), so the rate was 6%.

Commission vs. Markup

Commission pays a worker a share of a sales total, and the money goes to a person. A markup raises an item’s price above its cost, and the extra money stays with the business. A shop owner might use a markup to set the price and then pay a commission out of the revenue.

Markup

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