Ray's New Practical Arithmetic · Arts. 174–175 · Unit 15: Applications of Percentage: Mercantile Transactions
82. Profit and loss
Goal: Your child finds the selling price, the cost, or the per cent of gain or loss, always using the cost as the base.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 210 defines Profit and Loss (Art. 174) with two worked examples and problems 3–7. Page 211 has problems 8–15 and the start of the Miscellaneous Examples (Art. 175), which continue on page 212.
The lesson, step by step
Warm-up
Ask: You buy lemons for 20¢ and sell lemonade made from them for 30¢. What is your profit? What fraction of your cost is it?
The idea
The cost is the price paid for goods.
The selling price is the price received for goods.
The cost is the base; the profit or the loss is the percentage; and the selling price is the sum or the difference of the base and percentage.
Work the book's examples
A merchant's profit on a piece of cloth which cost $40 is 10%: for how much does he sell it?
$40 + 10% of $40 = $44.
Prints that cost 6 ct. a yard are sold for 5 ct. a yard: what is the per cent of loss?
The loss is 1 ct. on a cost of 6 ct.: 1/6 = 16⅔%.
Guided practice
Do these together:
A grocer, by retailing coffee at 27 cents per pound, gains 12½%: what did it cost per pound?
A dealer sold two horses for $150 each; on one he gained 25%, and on the other he lost 25%: how much did he lose by the transaction?
The second surprises most people. Find each cost first ($120 and $200).
Independent practice and check
Your child works the rest of problems 3–15 and the Miscellaneous Examples on pages 211–212. 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: cost $10, sold $12, gain per cent? cost $8, gain 25%, selling price? sold for $9 at a 10% loss, cost?