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Math Word Problems for CBEST Exam Study Guide (page 6)

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Updated on Mar 29, 2011

1. 23 = 3 + 5N
2. 23 = 3 + 5N

Did you notice that the two problems were the same, but the second one was more wordy? If question 1 was easier, you can work word problems more easily by eliminating nonessential words. If question 2 was easier, you can work out problems more easily by picturing actual situations. If they were both equally easy, then you have mastered this section. Go on to the section on two-variable problems, which is a little more difficult.

Practice

If you found wordy word problems difficult, here are some more to try:

1. Sally bought 6 less than twice the number of boxes of CDs that Raphael (R) bought. If Sally bought 4 boxes, how many did Raphael buy?
2. A 1-inch by 13-inch rectangle is cut off a piece of linoleum that was made up of three squares in a row; each had N inches on a side. This left 62 square inches in the original piece of linoleum. How long was each of the sides of the square?
3. Six was added to the number of sugar cubes in a jar. After that, the number was divided by 5. The result was 6.How many sugar cubes were in the jar?

1. Sally = 2R – 6. Substitute 4 for Sally: 4 = 2R – 6
2. The first step is to find the dimensions of the original piece of linoleum by adding the area of the piece that was cut (1 × 13 = 13 square inches) to the area of the remaining piece: 13 + 62 = 75 square inches. If we use S to represent the length of a side of one square, then the area of the square is S2, and the area of all three squares is 3S2. The equation, then, will be 3S2= 75. Dividing both sides by 3, we get S2= 25. Finally, take the square root of each side to get S = 5. The length of each side is 5 inches.
3. = 6.Multiply both sides of the equation by 5, then subtract 6 from both sides of the equation: 5 () = 6 (5), 6 + N = 30, N = 24. There are 24 sugar cubes in the jar.

Three Success Steps for Problems with Two Variables

When turning "as many as" sentences into equations, consider the following steps.

1. Read the problem to decide which variable is least.
2. Combine the number given with the least variable.
3. Make the combined number equal to the larger amount.

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.