Ray's New Practical Arithmetic · Arts. 170–172 · Unit 15: Applications of Percentage: Mercantile Transactions
80. Applications of percentage: commission
Goal: Your child knows the words agent, principal, commission and net proceeds, and works commission problems with the percentage cases.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 205 sorts the applications of percentage (Art. 170) and gives a general rule. Page 206 defines Mercantile Transactions (Art. 171) and agents (Art. 172). Page 207 defines commission and works examples, and page 208 finishes the problems. Answers are printed.
The lesson, step by step
Warm-up
Ask: If someone sells your bike for you and keeps $5 of every $100, how much do they keep on a $60 sale?
The big picture
The applications of Percentage may be divided into two classes: (1) Those without the element of time; (2) those with the element of time.
The general rule says to find which numbers are the base, percentage, and their sum or difference, then use the right case.
The words
An agent is a person intrusted with the business of another.
The commission is the sum paid an agent for transacting business.
The net proceeds is the sum remaining after deducting the commission and charges.
The value of the goods is the base; the commission is the percentage.
Work the book's examples
An agent whose commission is 5%, receives how much upon a sale of goods amounting to $240?
Case I: .05 × $240 = $12.
An agent receives $210 with which to buy goods: after deducting his commission of 5% what sum must he expend?
This is Case IV, since $210 is the goods plus 5% of them. $210 ÷ 1.05 = $200.
Guided practice
Do these together:
An auctioneer received $11.50 for selling a lot of goods amounting to $460: what per cent commission did he receive?
What are the net proceeds on a sale of goods amounting to $180, at 4% commission?
Independent practice and check
Your child works the remaining commission problems on pages 207–208. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: 2% of $500; 5% of $60; a 10% commission was $7, so the sale was how much?
Tip
Old business note: a "commission merchant" or "factor" sold goods for farmers and makers far away and sent back the money after taking a share. Today real-estate agents and many salespeople are still paid this way.