How do you calculate ratios? Example question: 'White paint costs £2.80 per litre, Blue paint costs £3.50 per litre, White paint and blue paint are mixed in the ratio 3:2. Work out the cost of 18 litres of the mixture [4 marks]' AQA Mathematics (8300)

Firstly, we need to calculate how much of the mixed paint is going to be white paint and how much is going to be blue paint. We can do this by looking at the ratio 3:2, if we add up the numbers in the ratio (3+2=5) and then divide the total amount of paint by this number (18/5=3.6). From this we have worked out that one unit (we can take the ratio of 3:2 as 3 units of white paint and 2 units of blue paint) is equal to 3.6 litres. Now we have calculated the value of one unit of paint we can work out how many litres of white and blue paint is in the mixed 18 litres of paint. If there are 3 units of white paint in the mixture, the the total amount is going to be 3 times 1 unit (3x3.6=10.8 litres), and likewise for the blue paint, there is going to be 2 times one unit (2x3.6=7.2 litres). A simple check back to see if our values add up to 18 litres allow us to check if we have done this correctly - 10.8+7.2=18 litres - therefore we know we have done our ratio correctly. Now we have calculated the amount of white and blue paint of the mixture we can calculate the cost of both the white and blue paint. If one litre of white paint cost £2.80, then the cost of the amount of white paint we need is going to be cost of one litre multiplied by how many litres we need (2.80x10.8=30.24) - so the cost of the white paint is £30.24. The same rule can be applied for the blue paint - 3.50x7.2=£25.20. We have not finished though, the question asks for the TOTAL cost of 18 litres so we need to add up the cost of both the white and blue paint in the mixture (£30.24+£25.20=£55.44), giving the total cost to be £55.44 - this is our answer.