00:01
In this question, we want to make 10 ounces of an 8 .5 % hydrochloric acid solution by mixing a 5 % solution, a 20 % solution, and water.
00:13
We want to find how much of each of these three we need to use in order for the amount of water to be the same as the total amount of hydrochloric acid used, both 5 % and 20%.
00:25
To start answering this question, let's assign variables to the numbers we want to find.
00:33
If we call the amount of 5 % solution and 20 % solution x and y, then we know that from the condition of the question that the amount of water has to be the same as the amount of total hydrochloric acid solution used, that the amount of water is x plus y.
00:56
Now we can form a system of two equations to solve for these two variables.
01:06
From the chart, we know that we can form one equation by using the volumes, because we know the total volume x plus y plus x plus y is going to equal 10.
01:20
But we also need one more equation.
01:24
And so since we know the concentrations, we can find the volumes of acid, of pure acid in each solution and equate the sum of these volumes.
01:38
To the amount of pure acid in the resulting mixture...