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# Math Word Problems for CBEST Exam Study Guide (page 5)

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Updated on Mar 29, 2011

### Problems with Two Variables

In solving problems with two variables, you have to watch out for another backwards phrase: as many as.

#### Sample Two-Variable Questions

The following equations require the use of two variables. Choose the answers from the following:

1. 2x = y
2. 2y = x
3. 2 + x = y
4. 2 + y = x
5. none of the above
1. Twice the number of letters Joey has equals the number of letters Tina has. Joey = x, Tina = y.
2. Tuli corrected twice as many homework assignments as tests. Homework = x, tests = y.

1. a. Equals is the verb. Joey, or x, is on one side of the verb; Tina, or y, is on the other. A straight rendering will give you choice a, or 2x = y, because Tina has twice as many letters as Joey has. To check, plug in 6 for y. If Tina has 6 letters, Joey will have 6 ÷ 2, or 3 letters. The answer makes sense.
2. b. Corrected is the verb. Which did Tuli correct fewer of? Tests. You need to multiply 2 times the number of tests to reach the number of homework assignments. Check: If there are 6 tests, then there are 12 homework assignments: 2 × 6 = 12. This answer makes sense.

#### Practice

Now that you are clued in, try the following using these same answer choices.

1. 2x = y
2. 2y = x
3. 2 + x = y
4. 2 + y = x
5. none of the above
1. Sandra found two times as many conch shells as mussel shells. Conch = x, mussel = y.
2. Sharon walked two more miles today than she walked yesterday. Today = x, yesterday = y.
3. Martin won two more chess games than his brother won. His brother = x, Martin = y.

1. b.
2. d.
3. c.