Ray's New Elementary Algebra · Art. 161 · Unit 4: Chapter IV: Simple equations
31. Problems with two unknowns
Goal: Your student writes two equations for a problem with two unknowns and solves them.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
- A card to cover printed answers
What's in the book
When to use two letters, two problems solved both ways, the digits problem, and exercises 5 to 34 with printed answers. A general review follows.
The lesson, step by step
Warm-up
Solve x + y = 25 and x − y = 9. (17 and 8.)
One letter or two?
Read Art. 161 and problem 1, solved first with one unknown, then with two. Ask: Which way felt clearer?
Digit problems
Read problem 3. Say: A two-figure number with tens digit x and units digit y is 10x + y. Reversed, it is 10y + x.
Guided practice
Your student sets up and solves:
5. A grocer sold to one person 5 lb. of coffee and 3 lb. of sugar, for 79 cents ; and to another, at the same prices, 3 lb. of coffee and 5 lb. of sugar, for 73 cents ; what was the price of a lb. of each? Ans. Coffee 11 cts., sugar 8 cts.
17. A said to B, "give me $100, and then I shall have as much as you." B said to A, "give me $100, and then I shall have twice as much as you." How much had each? Ans. A $500, B $700.
Independent practice
Choose eight to ten of exercises 6 to 34. Good ones: 6, 9, 13, 14, 19, 20, 21 and 24.
Review
Use the General Review on p. 125 as an oral quiz.
Wrap-up
Your student explains, for one problem, which two facts gave the two equations.
Tip
Two unknowns need two separate facts from the problem. Have your student underline them before writing anything.
Answers to the book's problems
The book prints the answer after each exercise.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.