J.R. S. answered • 07/02/25
Ph.D. University Professor with 10+ years Tutoring Experience
There are a number of ways to answer this question. Below, I present 2 of the common methods.
First method is referred to as alligation. It is typically used in pharmaceutical calculations but is applicable here as well. In this method you list what you have on the left of a grid (10% and 55%) and what you want (50%) in the center. Then you take the difference diagonally and place that value on the right side of the grid. This value represents the PARTS of the corresponding solution. This will be evident from the grid below...
HAVE....... WANT....... PARTS
10 ..................................5................
....................50................................
55................................ 40...............
So, you would take 5 parts of the 10% solution + 40 parts of the 55% solution. This makes 45 parts of the desired 50% solution. Since the question doesn't state a final volume of the 50% solution, you could mix 5 L of 10% with 40 L of 55%, or 0.5 L with 4.0 L, or 0.005 L with 0.04 L, etc.
In a second method, you simply use algebra to solve this. But to do so, we need to assume a final volume of the 50% solution. We can pick any value, so let's say 1 liter is our desired final volume of 50% HCl
(x L)(10%) + (1 L - x L)(55%) = (1L)(50%)
10x + 55 - 55x = 50
-45x = - 5
x = 0.11 L and this is the volume of 10% HCl
Since we chose to make 1 L, the volume of 55% is 1 - 0.11 = 0.89 L
So you would mix 0.11 L of 10% HCl with 0.89 L of 55% HCl to make 1 L of 50% HCl
Does this agree with the first method? Here the ratio of 55% to 10% is 0.89 L/0.11 L = 8:1
The ratio in the above alligation method is 40 L / 5 L = 8:1
Pick your poison on which method you choose to use.
