How to Solve Mixture Problems Part 1

If you have followed this blog, then you would know that we have been tackling a lot of math word problems. In this series, we will learn to solve another type of math word problem called mixture problems. Mixture problems are easy if you know how to set up the equation.

Mixture problems can be classified into two, those which deals with percent and the other which deals with price. In any case, the method of solving is almost the same. Of course, in working with percent, you must be able to know the basics of percentage problems. Let’s have our first example.

Example 1

How many ml of alcohol does a 80 ml mixture if it contains 12% alcohol?

Solution and Explanation

In this example,the word mixture means that alcohol is mixed with another liquid (we don’t know what it is and we don’t need to know). The total mixture contains 80 ml and we are looking for the pure alcohol content which is 12% of the entire mixture. Therefore,

pure alcohol content = 12%× 80 ml = 0.12 x 80 ml = 9.6 ml

In the calculation above, we converted percent to decimal (12% to 0.12) and then multiply it with 80. This means that in the 80 ml alcohol, 9.6 ml is pure alcohol.

Example 2

What is the total alcohol content of an 80 ml mixture containing 12% alcohol and a 110 ml mixture containing 8% alcohol?

Solution and Explanation

In this problem, we need to “extract” the pure alcohol content of both mixtures and add them in order to find the volume of the pure alcohol content of both mixtures.

In Example 1, we already know that it contains 9.6 ml of alcohol, therefore, we only need to solve for the second mixture.

Pure alcohol content of Example 2 = 8% × 110 ml = 0.08 x 110 ml = 8.8 ml

In the calculation above, we converted 8% to decimal so it became 0.08. Multiplying 0.08 by 110 gives us 8.8 ml. Therefore,

total alcohol content = 9.6 ml + 8.8 ml = 18.4 ml.

That means that the two mixtures contain 18.4 ml of pure alcohol in total.

The second problem shows that if we have more than one mixture, and we want to find the total amount of pure content, then we need to add the pure contents in the mixtures. Now, does the percentages add up? Will the total mixture contain 20% alcohol? Let’s see.

The total amount of liquid = 110 ml + 80 ml = 190 ml
Total amount of alcohol = 18.4 ml

18.4 ml / 190 ml = 0.0968

As we can see, if we convert 0.0968 to percent, it becomes 9.68% and not 20%. In what case will they add up?

We will use the concepts we have learned in these two problems to solve more complicated problems in the next post. Stay tuned by subscribing in the email subscription box on the right part of the page.