71. Commission: Cases III and IV

The lesson, step by step

1. Warm-up

   Quick Case I review: 3% commission on a $2400 sale. ($72; the owner gets $2328.)

2. Case III

   Read:

   Given the commission and rate, to find the sum on which commission is charged.

   Divide the commission by the rate. Work:

   My commissions in 1 year, at 2½%, are $3500: what were the sales, and the whole net proceeds?

   $3500 ÷ .025 = $140000 of sales; $140000 − $3500 = $136500.

3. Case IV

   Read:

   Given the rate of commission and the net proceeds or the whole cost, to find the sum on which commission is charged.

   When an agent buys, the whole cost = purchase + commission. When an agent sells, the net proceeds = sale − commission.

4. Work the book's example

   Sent $1000 to buy a carriage, commission 2½%: what must the carriage cost?

   Read the book's hint:

   100% + 2½% = 102½% = $1000; find 1%, then 100%.

   $1000 ÷ 1.025 = $975.61. Check: 2½% of $975.61 is $24.39, and $975.61 + $24.39 = $1000.

5. Guided practice

   Together:

   A lawyer collects a debt for a client, takes 4% for his fee, and remits the balance, $207.60: what was the debt and the fee?

   Here the client gets 96% of the debt.

6. Independent practice

   Your student finishes the examples for both cases.

7. Check and wrap-up

   Check the printed answers. Ask: Why can't we just take 2½% of $1000? (The commission is figured on the carriage's price, not on the $1000.)