Ray's New Higher Arithmetic · Arts. 242–245 · Unit 15: Percentage: Profit and Loss, Stocks and Bonds

65. Profit and loss: finding profit and rate

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

⏱ About 45 minutes · 8 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

Profit and loss defined (cost, selling price, profit, loss), the four cases matched to the four cases of percentage, Case I (cost and rate given) with examples, and Case II (cost and profit or loss given, find the rate) with examples. Answers are printed for nearly all.

The lesson, step by step

  1. Warm-up

    Mental: Bought for $20, sold for $25. Profit? What per cent of the cost?

  2. The idea

    Read:

    Profit and Loss are commercial terms, and presuppose a cost price.

    Profit is the excess of the Selling Price above the Cost.

    Loss is the excess of the Cost above the Selling Price.

    There are four cases of Profit or Loss, solved like the four corresponding cases of Percentage.

    The cost is the base.

  3. Case I

    Read:

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

    The book's example: $4800 invested at 13% profit gives $624.

  4. Guided practice

    Together:

    If a man invests $1450 so as to gain 14 1/2%, what is his profit?

    I bought $1760 worth of grain, and sold it so as to make 26 1/4% profit.

    ($210.25; the grain sold for $2222.)

  5. Case II

    Read:

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

    The book's example: a mine bought for $45000 and sold for $165000 gains $120000, which is 266⅔% of the cost. Then:

    If I buy at $1 and sell at $4, how many per cent do I gain?

    (300%.)

  6. Independent practice

    Your student works the rest of the Case I and Case II examples.

  7. Check

    Answers are printed. Case II, Example 5 (a farm that loses value and is then sold and reinvested) has no clear printed answer in the scan; work it together on the page and talk through what "the entire transaction" means.

  8. Wrap-up

    Ask: Why is the rate always figured on the cost, not the selling price? (The cost is the base, the money put in.)

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