Question

A 40% acid solution is to be mixed with a 60% solution to get 100 liters of 55% solution. How many liters of EACH solution should be used?

Answer 1

It may help to think of the amount of acid in some sort of imaginary units. For example, the 40% solution has 40 acids for every 100 waters (assuming the solvent is water). So you want the final solution to have 55 acids for every 100 waters in 100 liters. We can arbitrarily say that 1 liter of this solution contains 5.5 acids and 10 waters to make the numbers smaller. So if that is the case, all 100 liters will have 550 acids and 1000 waters.

Answer 2

Now for finding the exact amount of each solution required, first let's realize that the final solution has to contain more of the 60% solution than the 40% (since 55% is much closer to 60 than 40).

Answer 3

Actually I just found an easier way to solve this

Answer 4

We know that we want 55% in the end, and the difference in concentration between the two solutions is 20%. 55% is 5% away from 60%, or 15% away from 40%. That means that the final solution will be more composed of the 60% solution with a ratio of 3 to 1 [15/5 = 3/1]. So just inflate that ratio to the 100 liters, and you will find that the set of numbers that add up to 100 that have a ratio of 3 to 1 is 75 and 25. There are 75 liters of the 60% solution, and 25 liters of the 40%.

Answer 5

Sorry if you didn't want the answer itself, I was having trouble explaining without giving away the answer.

Answer 6

No it is ok you explained it really well for me thank you