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# Word Problems and Data Analysis: GED Test Prep

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Updated on Mar 9, 2011

Many students struggle with word problems. In this article, you will learn how to solve word problems with confidence by translating the words into a mathematical equation. Because the GED Mathematics Exam focuses on real-life situations, it's especially important for you to know how to make the transition from sentences to a math problem.

### Translating Words into Numbers

The most important skill needed for word problems is the ability to translate words into mathematical operations. This list provides some common examples of English phrases and their mathematical equivalents.

• Increase means add.
• A number increased by five = x + 5.

• Less than means subtract.
• 10 less than a number = x – 10.

• Times or product means multiply.
• Three times a number = 3x.

• Times the sum means to multiply a number by a quantity.
• Five times the sum of a number and three = 5(x + 3).

• Two variables are sometimes used together.
• A number y exceeds five times a number x by ten.

y = 5x + 10

• Inequality signs are used for at least and at most, as well as less than and more than.
• The product of x and 6 is greater than 2.

x × 6 > 2

When 14 is added to a number x, the sum is less than 21.

x + 14 < 21

The sum of a number x and 4 is at least 9.

x + 4 ≥ 9

When seven is subtracted from a number x, the difference is at most 4.

x – 7 ≤ 4

### Assigning Variables in Word Problems

It may be necessary to create and assign variables in a word problem. To do this, first identify an unknown and a known. You may not actually know the exact value of the "known," but you will know at least something about its value.

Examples

Max is three years older than Ricky.

Unknown = Ricky's age = x. Known = Max's age is three years older.

Therefore, Ricky's age = x and Max's age = x + 3.

Lisa made twice as many cookies as Rebecca.

Unknown = number of cookies Rebecca made = x.

Known = number of cookies Lisa made = 2x.

Cordelia has five more than three times the number of books that Becky has.

Unknown = the number of books Becky has = x.

Known = the number of books Cordelia has = 3x + 5.

### Ratio

A ratio is a comparison of two quantities measured in the same units. It can be symbolized by the use of a colon—x : y or or x to y. Ratio problems can be solved using the concept of multiples.

Example

A bag containing some red and some green candies has a total of 60 candies in it. The ratio of the number of green to red candies is 7:8.How many of each color are there in the bag?

From the problem, it is known that 7 and 8 share a multiple and that the sum of their product is 60. Therefore, you can write and solve the following equation:

7x + 8x = 60

15x = 60

Therefore, there are 7x = (7)(4) = 28 green candies and 8x = (8)(4) = 32 red candies.

### Mean, Median, and Mode

To find the average, or mean, of a set of numbers, add all of the numbers together and divide by the quantity of numbers in the set.

Example

Find the average of 9, 4, 7, 6, and 4.

(Divide by 5 because there are 5 numbers in the set.)

To find the median of a set of numbers, arrange the numbers in ascending order and find the middle value.

• If the set contains an odd number of elements, then simply choose the middle value.
• Example

Find the median of the number set: 1, 3, 5, 7, 2.

First arrange the set in ascending order: 1, 2, 3, 5, 7,and then choose the middle value: 3. The answer is 3.

• If the set contains an even number of elements, simply average the two middle values.
• Example

Find the median of the number set: 1, 5, 3, 7, 2, 8.

First arrange the set in ascending order: 1, 2, 3, 5, 7, 8, and then choose the middle values, 3 and 5.

Find the average of the numbers 3 and 5:

= 4. The median is 4.

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