Ray's New Intellectual Arithmetic · Lesson LXVIII · Unit 8: Percentage and interest
68. Finding the cost from the selling price
Goal: Your child works backwards from a selling price and a per cent gain or loss to the cost.
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
Twenty problems. The model: a watch sold for $12 at a 20 per cent gain cost $10, because the price is 120 hundredths, or 6/5, of the cost.
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
SayA 20 per cent gain means the price is the cost and one-fifth more: six-fifths of the cost. Six-fifths are $12, so one-fifth is $2, and the cost is $10.
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 watch was sold for $12, at a gain of 20 per cent: what did it cost?
A sold a watch to B for $60, gaining 20%; B sold it at a 20% loss: how much more did B lose than A gained?
Apples at 4 for 3 cents give a 50% gain: what is the gain at 5 for 4 cents?
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.
Answers to the book's problems
1) $10. 7) 3 cents. 8) $4 gain (50%). 9) 25% loss. 10) 50% gain. 11) $4.50 loss. 12) B lost $2 more. 14) 60%. 15) 16⅔% loss.
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 ↗.