Ray's New Intellectual Arithmetic · Lesson LXIX · Unit 8: Percentage and interest
69. Discounts: “per cent off”
Goal: Your child works out prices with a discount, and with two discounts one after another.
You'll need
- The book page (press “📖 Book page”, or use a printed copy)
- Paper for jotting, though the work is meant to be done in the head
What's in the book
Ten problems. The book explains “10 per cent off” and “20 and 5 off” (20 per cent off, then 5 per cent off what is left).
The lesson, step by step
Warm up
Ask three or four problems from the last lesson again, out of order. Your child answers and says why.
Show the reasoning
Say$500 at 20 and 5 off: 20 per cent off leaves $400; 5 per cent of $400 is $20, which leaves $380.
The second discount is taken off the reduced price, not the list price.
Work the problems aloud
Read each problem on the page aloud. Your child answers, then explains in a full sentence, the way the book's model solutions do. The problems go like this:
A $500 lot of books is sold at 20 and 5 off: what is paid?
Goods bought at 20 and 5 off cost $133: what was the list price?
On a $70 bill, 20 and 5 off is allowed on the first $50 and 10 and 5 off on the rest: what is paid?
Ask “Why?”
After each answer ask “Why?” or “How do you know?” Ray's wants the reasoning said aloud, not just the number. If your child stalls, go back to the model and say the first half of the explanation together.
Wrap up
Pick the two problems that were hardest today. Tomorrow, start with those as the warm-up.
Afterwards
Do the rest of the lesson's problems over the next day or two, a few at a time. Move on when your child can explain them without help.
Tip
A good one to try at a real sale: is “20% off, then 10% off” the same as 30% off? (It isn't: it's 28% off.)
Answers to the book's problems
1) $2.40. 4) $380. 6) $6. 8) $175. 10) $55.10.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in Ray's own Key ↗.