Solving Proportion Word Problems
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.  First, decide whether a comparison is being made.  That is often a good clue that you can set the problem up as a proportion.  Sometimes there will be clue words:  if..then, at this rate. You will also notice that there are 3 numbers given in the problem and you are asked to find the fourth.  The key to using proportions is setting up the problem carefully.  It is important to make sure that the numbers being compared are in the right order.


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 long as you put the same labels side by side:

          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 m stands for the unknown number of men.
       men          men
      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 m, which is the 3. 
960 ÷ 3 = 320
There are 320 men working in the hospital.

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
                          2

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 (3) 110 * 5 is correct.
                        2

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

Practice:

Be careful when answering these questions.  If the question includes the label in the problem, you do not need to include the label in the answer.

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?


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.