Mixing Paints

Topic:
Ratios

Introduction

In this activity you are going to explore the connection between ratio and percentages. Use the applet below to help you solve the problems.

Problem 1

You have mixed 5 litres of pink paint using red and white paint. The mixture is 60% red, but you actually wanted a 5 litre mixture of 80% red. How can you fix this without starting again. You can add red or white paint to your mixture. You can also pour some of your original mixture away, but not all of it. Answer to the following questions to help you find a solution.

Find the number of litres of white and red paint in the original 5 litres (60% red to 40% white)

What is the ratio of red to white paint in its simplest form?

We can't take white paint out of the mixture, so to get a higher percentage of red paint we need to add red.

Add (a) 1L (b) 3L (c) 5L of red paint. What percentage red paint does each one give?

Write each of these percentages as a ratio of red to white paint

You should have found that by adding 5 litres of red paint you get 10 litres of the desired 80% red mixture. However, this wastes 5 litres of paint as you only wanted 5 litres to begin with. Can you find a less wasteful way to get 5 litres of 80% red paint. (Hint: you need to pour some of the original mixture away first.

You are now going to investigate how to find different % of different quantities of paint, starting with the original 5 litres of 60%. Converting between ratio and percentage is one way you can do this. Thinking of the number of litres of each colour as the numbers in the ratio.