One of the uses for proportion is to solve real-world problems. In these, you are given a fact and asked to use it to find another amount.

**Example 1: 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 you know.

2 hours = 10 m^{2}

Step 2: Find the Highest common factor of the thing you know (10m^{2}) and the thing you are trying to find (25m^{2}). For this question, it would be 5.

2 hours = 10 m^{2}

1 hours = 5 m^{2}

^{(Note: Whatever you do to one side, you do to the other) }

^{Step 3: Use this to answer the question.}

1 hours = 5 m^{2}

5 hours = 25 m^{2}

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

This one is a bit more complicated

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

4 people = 3 hours = 60 cars.

The key thing to know here is that we only change two of the three quantities at once, we have to keep playing until we have the cars as 80 and the people as 2.

Change 1:

4 people = 3 hours = 60 cars

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.

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.

If half as many people are cleaning the same amount of cars, it will take twice as long.

2 people = 8 hours = 80 cars.