Ray's New Higher Arithmetic · Arts. 246–247 · Unit 15: Percentage: Profit and Loss, Stocks and Bonds

66. Profit and loss: finding the cost

Goal: Your student finds the cost from the profit and rate, and from the selling price and rate.

⏱ About 40 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Case III (profit or loss and rate given, find the cost), with the example of a lot sold at a profit of $423.50, and Case IV (selling price and rate given, find the cost), with the example of goods sold for $25.80 at a gain of 7½%; examples for practice with printed answers.

The lesson, step by step

  1. Warm-up

    Mental: I made $5, which was 25% of what I paid. What did I pay? ($20.)

  2. Case III

    Read:

    Given the profit or loss and the rate, to find the cost.

    The book's example: a lot sold for 34⅜% more than it cost gave a profit of $423.50. Divide the profit by the rate to get 1%, then multiply by 100. The cost was $1232. (Check: $1232 × .34375 = $423.50.)

  3. Case IV

    Read:

    Given the selling price (amount or difference) and the rate, to find the cost.

    The book's example: goods sold for $25.80, gaining 7½%. $25.80 is 107½% of the cost; $25.80 ÷ 1.075 = $24.

  4. Guided practice

    Together:

    Sold cloth at $3.85 a yard; my profit was 10%: how much a yard did I pay?

    Gold pens, sold at $5 apiece, yield a profit of 33 1/3%: what did they cost apiece?

    ($3.50; $3.75.)

  5. Independent practice

    Your student works the remaining examples for Cases III and IV.

  6. Check

    Answers are printed.

  7. Wrap-up

    Ask: A store sells a coat for $60 at a 20% profit. Is the cost $48? (No: $60 ÷ 1.20 = $50. 20% of the selling price is not 20% of the cost.)

@teddyrookbook GitHub