7.1 Solving ratio problems where the total is given

To understand how to solve ratio problems where the total is given, it's best to look through a worked example.

An art shop is ordering paint. They work out that they need to order red and blue paint in the ratio 3:4. They order a total of 56 cans of paint. How many of those cans are blue paint?

The first step to finding out, is to work out the total number of parts by adding together the parts of the ratio. If there are three parts red and four parts blue, that makes a total of seven parts altogether. Next, you need to work out what one part is worth. To do this, divide the total number of paint cans ordered, by the total number of parts. 56 divided by 7 equals 8. One part is worth eight cans.

Now, you know that one part of paint is 8 cans, you can work out what four parts are worth. 8 x 4 = 32. So the art shop needs to order 32 cans of blue paint.

Can you think of an extra check that you can carry out to confirm your answer? Well as you know what one part of paint is worth, you can also work out how many cans of red paint need to be ordered. 3 parts x 8 cans = 24 cans of red paint.

The total of red paint and blue paint should be 56. So you can check your answer by adding together the number of cans of each. 32 + 24 is indeed 56 cans.

So in summary, the steps for solving a ratio question like this are:

One. Add together the parts of the ratio. 3 + 4 = 7.

Two. Take the total amount given and divide by the sum of the ratio parts. 56 divided by 7 = 8.

Three. Finally, take the answer for step two, 8, and multiply by whichever part of the ratio you're interested in finding. 8 x 4 = 32.