1
The sum of two numbers is 67, and their difference is 5. Find the numbers.
Chapter 6 · Identities and Equations of Condition
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
0first-try
0of 10 done
From Solving Problems, exercise 12
Solve and check. Use the five steps.
From Representing Numbers, exercise 19
Represent each number.
2
One part of x + y is z. What is the other part?
From Identities and Transposition, exercise 16
Solve by transposing, then check.
3
Solve 3 - 5h + 2 = 7h + 5. What is h?
From Identities and Transposition, exercise 18
Solve by transposing, then check.
4
Solve 14x - 6x = 22 + 17x - 11x. What is x?
From Representing Numbers, exercise 15
Represent each number.
5
One part of x is 4. What is the other part?
From Solving Problems, exercise 6
Solve and check. Use the five steps.
6
What number, tripled and then diminished by 36, gives twice the original number?
From Representing Numbers, exercise 1
Represent each number.
7
Represent a number: Greater than n by 5.
From Representing Numbers, exercise 39
Represent each number.
8
A's age is x years, B's is 2x + 7, and C's is 3x - 8. Express (a) each age five years from now and (b) each age three years ago. Then write equations for: (c) In four years, A's and B's ages will add to 40. (d) Six years ago, C was 24 years older than A. (e) In 10 years A will be as old as B is now. (f) Four years ago C was as old as B will be in 10 years. (g) In x years B will be 40. (h) In 2 years their three ages will add to 100.
From Identities and Transposition, exercise 3
Solve by transposing, then check.
9
Solve 6y - 5 = 9y + 2. What is y?
From Representing Numbers, exercise 22
Represent each number.
10
The difference of two numbers is 18. If the greater is 34, what is the other?