Word Problems and Data Analysis: GED Test Prep (page 4)

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.

Mode

The mode of a set of numbers is the number that occurs the greatest number of times.

Example

For the number set 1, 2, 5, 3, 4, 2, 3, 6, 3, 7, the number 3 is the mode because it occurs the most often.

Percent

A percent is a measure of a part to a whole, with the whole being equal to 100.

• To change a decimal to a percentage, move the decimal point two units to the right and add a percentage symbol.

Example

.45 = 45%

.07 = 7%

.9 = 90%

• To change a fraction to a percentage, first change the fraction to a decimal. To do this, divide the numerator by the denominator. Then change the decimal to a percentage.

Example



• To change a percentage to a decimal, simply move the decimal point two places to the left and eliminate the percentage symbol.

Example

64% = .64

87% = .87

7% = .07

• To change a percentage to a fraction, put the percent over 100 and reduce.

Example



Keep in mind that any percentage that is 100 or greater will need to reflect a whole number or mixed number when converted.

Example

Here are some conversions you should be familiar with. The order is from most common to less common.

Calculating Interest

Interest is a fee paid for the use of someone else's money. If you put money in a savings account, you receive interest from the bank. If you take out a loan, you pay interest to the lender. The amount of money you invest or borrow is called the principal. The amount you repay is the amount of the principal plus the interest. The formula for simple interest is found on the formula sheet in the GED. Simple interest is a percent of the principal multiplied by the length of the loan:

Interest = principal × rate × time

Sometimes it may be easier to use the letters of each as variables:

I = prt

Example

Michelle borrows $2,500 from her uncle for three years at 6% simple interest. How much interest will she pay on the loan?

Michelle will pay $450 in interest.

Some problems will ask you to find the amount that will be paid back from a loan. This adds an additional step to problems of interest. In the previous example, Michelle will owe $450 in interest at the end of three years. However, it is important to remember that she will pay back the $450 in interest as well as the principal, $2,500. Therefore, she will pay her uncle $2,500 + $450 = $2,950.

In a simple interest problem, the rate is an annual, or yearly, rate. Therefore, the time must also be expressed in years.

Example

Kai invests $4,000 for nine months. Her investment will pay 8%. How much money will she have at the end of nine months?

Kai will earn $180 in interest.

Probability

Probability is expressed as a fraction and measures the likelihood that a specific event will occur. To find the probability of a specific outcome, use this formula:

Example

If a bag contains 5 blue marbles, 3 red marbles, and 6 green marbles, find the probability of selecting a red marble:

Helpful Hints about Probability

• If an event is certain to occur, the probability is 1.
• If an event is certain not to occur (impossible), the probability is 0.
• If you know the probability of all other events occurring, you can find the probability of the remaining event by adding the known probabilities together and subtracting their total from 1.

General Strategies for Math Questions

• Skipping and returning.

If you are unsure of what you are being asked to find, if you don't know how to solve a problem, or if you will take a long time to find the correct answer, skip the question and come back to it later. Do the easy problems first. The GED Mathematics Exam is not arranged with increasingly difficult questions. The difficult questions appear alongside of the easier questions. Therefore, it is important to skip difficult problems and come back to them.

• Plugging in.

There will be times when you should use the answer choices to find the correct answer. This can be done when you have a problem that gives you a formula or equation. Plug in answers when you feel it will be quicker than solving the problem another way, and when you have enough information to do so.

• Eliminating.

Eliminate choices you know are wrong so that you can spend more time considering choices that might be right. It may sound like a simple strategy but it can make a big difference.

• Making educated guesses.

It's important to remember you are not penalized for a wrong answer. If you don't know the answer to a question and you are approaching the time limit, simply use the last few minutes to make an educated guess to the remaining questions. You can surely eliminate some of the answer choices and improve your odds of getting it right.