Solve Real Life Proportion Questions

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 m² of grass, how long does it take to cut 25 m² of grass?

Step 1: Write out the proportion we already know.

2 hours = 10 m²

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 m²

1 hour = 5 m²

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 m²

5 hours = 25 m²

So it takes 5 hours to mow 25 m² 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.