Ray's New Higher Arithmetic · Misc. Exercises 36–78 · Unit 29: Miscellaneous Exercises
126. Miscellaneous exercises, part 2
Goal: Your student solves mixed problems on clocks, work, measures, roots and investments.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Problems 36 to 78: clocks, boats and currents, pasture, cubes and circles, interest and investments. Most answers are printed.
The lesson, step by step
Warm-up
Review the routine from the last lesson: read twice, restate, name the method, estimate, work, check.
Work one together
A boat makes 15 mi. an hour down stream, and 10 mi. an hour up stream: how far can she go and return in 9 hr.?
Each mile down and back takes 1/15 + 1/10 = 1/6 of an hour. In 9 hours: 54 miles.
Guided practice
I can pasture 10 horses or 15 cows on my ground; if I have 9 cows, how many horses can I keep?
What is the side of a cube which contains as many cubic inches, as there are square inches in its surface?
A geometry one
The boundaries of a square and circle are each 20 ft., which is the greater, and how much?
This ties back to the circle lesson.
Independent practice
Your student works a selection, including one investment problem such as:
Invested $10000; sold out at a loss of 20%: how much must I borrow at 4%, so that, by investing all I have at 18%, I may retrieve my loss?
Check and wrap-up
Check the printed answers (and the two below). Ask your student which chapters these problems came from.
Afterwards
Several short sittings.
Answers to the book's problems
Ex. 36 (answer not printed in the scan): 7 men do the work in the given time, so 10 men need only 7/10 of their time; each can rest 3/10 of his time. Ex. 78 (answer not printed in the scan): $2700 at 25% discount buys $3600 of stock, paying 8%, or $288 a year. To get $288 at 10%, buy $2880 of stock; at 4% discount it costs $2880 × .96 = $2764.80.
Worked out for this site from the scan. If a number in your copy differs, trust the book.