Proportion Word Problem Examples

The real power of proportions is here: solving word problems! There are about a billion billion examples of times in real life when you could use a proportion to solve a problem. The following examples will show you a few examples of different types of problems you might encounter. We'll start with a more basic problem:

Example 1

You are at Superstore, and you see that 5 oranges cost $2.35. You need 26 oranges to make a huge fruit salad. How much will 26 oranges cost?

Solution

There are two important pieces of this question. They are:

5 oranges cost $2.35
and
How much will 26 oranges cost?

You can ignore everything else! Notice that the first sentence above can be written as a ratio. Let's write it now as oranges:$.

We could have written the ratio in the other order ($:oranges) but you will find it does not matter. (This will be proved later.) Now the 2nd important piece of the puzzle has to be used. How much will 26 oranges cost? We can write this as another ratio (with an unknown) and create a proportion with our two ratios:

Notice that the number of oranges went on the top of the ratio. This is because we put oranges on the top of our original ratio. Things that are the same should be on the same level (top or bottom) of the proportion.

We do not know (yet) how much money 26 oranges cost, so we put an x (or any other variable you like) where money goes in this example, on the bottom.

Recognize a proportion when you see one? You should know how to solve a proportion by now using cross multiply and divide so let's solve for x. (If you forget how to cross multiply and divide to solve a proportion, click here).

Using cross multiply and divide we get:

This means that 26 oranges will cost $12.22.

To prove to you that it doesn't matter HOW you set up the original ratio let's do this question again upside down:

Notice that in this example, oranges are on the bottom and money is on the top. The cross multiplication, however, remains the same:

And we get the same answer of $12.22!

Example 2

It takes 13 people to pull a 20 ton bus. How many people would it take to pull a 135 ton semi-trailer truck?

Solution

Set up the first ratio. Notice that we are going to put people on top:

Now, remembering that people are on the TOP of the proportion, set up this proportion with the 135 ton weight and the unknown number of people.

Notice we used the variable p for people. Now use cross multiply and divide to solve for the number of people. You should get:

There is a small problem with our answer...you can't have 0.75 of a person! So round up, and our answer is 88 people to pull a 135 ton semi-trailer truck.

That's it for the examples. For extra help on proportion word problems consult your booklet or ask your teacher. If you like, you can move on to the word problem worksheet or go back to the proportion main page.