One of the most common uses for **proportion** in maths is to solve real-world problems.

In these, we will be given a fact and asked to use it to find another amount.

Let's look at this in action now.

**e.g. If it takes 2 hours to cut 10 m ^{2} of grass, how long does it take to cut 25 m^{2} of **

**grass?**

**Step 1: **Write out the proportion we already know.

2 hours = 10 m^{2}

**Step 2: **Find the Highest Common Factor (HCF) of the proportion we already know and the element we are trying to find.

2 hours = 10 m^{2}

1 hour = 5 m^{2}

Note: Whatever we do to one side, we need do to the other which, in this case, this is ÷ 2.

**Step 3: **Use the information we have found to answer the question.

1 hour = 5 m^{2}

5 hours = 25 m^{2}

**So it takes 5 hours to mow 25 m ^{2} of grass, based on the current proportion provided. **

**e.g. 4 people take 3 hours to clean 60 cars. How long will it take 2 people to clean 80 cars?**

This one is a little more complicated as we have **three variables** present.

Our first step is to write out what we know as an equation:

4 people = 3 hours = 60 cars

The key step to apply here is that we can **only** change **two of the three quantities** at once.

We need to keep testing and making changes to two elements at a time, until we have the cars as 80 and the people as 2.

Change 1:

4 people = 3 hours = 60 cars ÷ Both by 3

So if the same amount of people are cleaning one-third of the cars, it will take one-third of the time:

4 people = 1 hour = 20 cars

Change 2:

4 people = 1 hour = 20 cars × Both by 4

So if the same amount of people are cleaning 4 times as many cars, it will take them 4 times as long:

4 people = 4 hours = 80 cars

Change 3:

4 people = 4 hours = 80 cars ÷ People by 2, doubles the hours required

So if half as many people are cleaning the same amount of cars, it will take twice as long:

2 people = 8 hours = 80 cars

**So based on the proportion given, it will take 2 people 8 hours to clean 80 cars. **

In this activity, we will solve real life proportion problems with two or more variables using the methods shown above of applying and manipulating the information provided in the question.