Math 6 Honors (Period 6 and 7)

Problem Solving: Using Proportion 7-8

Proportions can be used to solve word problems. Use the following steps to help you in solving problems using proportions
~ Decide which quantity is to be found and represent it by a variable
~ Determine whether the quantities involved can be compared using ratios (rates)
~ Equate the ratios in a proportion
~ Solve the proportion

Mr. Kaiser bought 4 tires for his car at a cost of $264. How much would 5 tires cost at the same rate?
Let c = the cost of 5 tires. Set up a proportion

4/264 = 5/c
Solve the proportion
4c = 5(264)
Now divide both sides by 4
4c/4 = 5(264)/4
c = 330
Therefore, 5 tires would cost $330

Notice, the proportion in this example could also have been written as

2/264 = c/5
In fact--Any of the following proportions can be used to solve the problem

4/5 = 264/c 5/4 = c/264 4/264 = 5/c 264/4 = c/ 5
All of the above proportions result in the same equation

4c = 5(264)
But be careful you need to use a proportion that does relate.
4/5 DOES NOT EQUAL c/264. That is not an accurate proportion and would result in an inaccurate solution.

tires ___________ = _____________tires
cost _____________=_____________cost

For every 5 sailboats in a harbor, there are 3 motorboats. If there are 30 sailboats in the harbor, how many motorboats are there?

Let m = the number of motorboats
5/3 = 30/m

5m = 3(30) divide both sides by 5 5m/5 = 3(30)/5


m=18
There are 18 motorboats in the harbor.

Some guidelines you can use to determine when it is appropriate to use a proportion to solve a word problem.

Ask the following questions

If one quantity increase does the other quantity also increase? (If one quantity decreases, does the other quantity decrease?) When the number of tires is increase, the cost is also increased.

Does the amount of change (increase or decrease) o one quantity depend upon the amount of change (increase or decrease) of the other quantity? The amount of increase in the cost depends upon the number of additional tires bought.

Does one quantity equal some constant times the other quantity? The total costs equals the cost of one tire times the number of tires. The cost of one tire is constant.

If the answers to all the questions above is YES, then it is appropriate to use a proportion.

Sometimes setting up a table can be useful




Although the problems in this lesson may be solved without using proportions, I must insist that you write a proportion for each problem and solve using this method. You may check your work using another other method you know.