Proportion Word Problems |
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Many of the word problems on the high school equivalency test can be solved using proportion. Sometimes it’s hard to recognize which problems can be solved that way.

Study the following examples. Notice how the parts of the proportion are set
up.

**Example 1: ** If 12 yards of lumber
cost $40, how much do 30 yards cost?

** Step 1: **In this problem you are comparing yards
to cost. Set up two ratios—yards are on the top of each ratio. Cost is on
the bottom. Actually it would not matter if you put cost on the top and yards
on the bottom as

__Yards__
__yards__ **or** __cost __ __cost__

Cost cost
yards yards

__12__ __30__
__40__ __c
__ 40 c 12 30

Either way you set it up, you will be multiplying 40 by 30 and then dividing by 12. So don’t worry too much about the way you set up the problem, as long as like labels are next to each other. I usually just write the problem in the order that I read it.

** Step 2:** Find the cross product of 40 and 30

40 * 30 = 1200

** Step 3: **Divide your answer from Step 2, 1200,
by the other number in the proportion, 12.

1200 ÷ 12 = 100

The cost of 30 yards of lumber in $100.

**
Example 2: **The ratio of the number
of men to the number of women working in a certain hospital is 2:3. If 480
women work in the hospital, how many men work there?

** Step 1: **Make a proportion comparing men to
women. The top number in each ratio refers to men. The bottom number refers
to women. Here

women women

__2__ = __ m __

3 480

** Step 2: ** Find the cross products of 2 and 480.

2 * 480 = 960

** Step 3:** Divide 960 by the number opposite
the

960 ÷ 3 = 320

There are

In some cases on the high school equivalency test, you may have to recognize how a proportion problem should be set up rather than find the solution itself. The next example shows this type of problem.

**Example 3: **Manny
drives 110 miles in 2 hours. Which expression below shows the distance he can
go in 5 hours if he drives at the same speed?

**1) **__5 * 2
__ 110

**
2) **__110 *
2
__ 5

**3)**__ 110 * 5
__ 2

**4) **__100 + 5
__ 2

** Step 1: **Make a proportion. The top number is miles, and the
bottom number is hours. Remember that this order can be reversed as long as
you reverse it on the second fraction, also.

__110__
= __m
__ 2 5

** Step 2: **Show how you would multiply to find the first cross
product.

**110
* 5**

** Step 3: **Show how you would divide to find the missing number.

__110
* 5
__

** Step 4: **Choose the solution that shows the cross product of
110 and 5 divided by the other number in the proportion -- 2. This is an example
of a “set-up” question that you will see on the high school equivalency test.

Choice

Notice that choice **(4) **is wrong because it shows
the *sum* instead of the *product* of 110 and 5.

**1. ** The ratio of lime to sand in a mixture
of concrete is 1:3. Jeff is using 12 pounds of sand in the mixture of concrete.
How much lime should he use?

**2. ** Cindy gets paid an hourly wage. During
a 40-hour week, Cindy earns $240. This week she worked only 35 hours. How
much did she earn?

**3. ** If 12 cans of soda cost $4.50, how
much do 30 cans cost?

**4. ** Six feet of lumber weighs 15 pounds.
What is the weight of 16 feet of the same lumber?

**5. ** The ratio of girls to boys at the Oakdale
School is 5:4. There are 120 girls in the school. How many boys are there?

**6. ** Carla makes $52.80 in 8 hours. How
much does she make in 20 hours?

**7. ** If 12 acres yield 1440 bushels of corn,
how many bushels of corn can a farmer expect from a 50-acre field?

**8. ** The ratio of the width to the length
of a snapshot is 3:5. If the snapshot is enlarged to be 15 inches wide, how
long will it be?

**9. ** Manny drove 72 miles in 1˝ hours.
If he drives at the same average speed, how many miles can he go in 4 hours?

**10. ** The scale on a map is ˝ inch = 15 miles. How far apart are
two towns that are 2 inches apart on the map?

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Here are some more proportion word problems to practice on:

http://www.edhelper.com/math/math_sixth_grade_SIX64.htm

http://www.algebrahelp.com/lessons/proportionbasics/

**Resources:**

__GED Test 5: Mathematics__. (2001). Contemporary Books, NTC/Contemporary
Publishing Group: Lincolnwood, IL.

Howett, Jerry. (1998). __GED Program: Mathematics__. Cambridge
Adult Education: Upper Saddle River, NJ.

__Pre-GED: Mathematics__. (2000). Steck-Vaughn: Austin, TX.