A chemist has a 55% acid solution and a 40% acid solution. How many liters of each should be mixed in order to produce 100 liters of a 46% acid solution?
Let $X_1$ denote the total amount of acid solution 1. Let $X_2$ denote the total amount of acid solution 2. Now, the total amount of solution is $X_1 + X_2$. So we want $$X_1 + X_2 = 100.$$ Now for the acid content. Here, we'll have $0.55X_1$ liters of acid from the first solution, and $0.40X_2$ liters of acid from the second solution. Our second condition says we want $$0.55X_1 + 0.40X_2 = 0.46*100 = 46.$$ So we have a system with two equations. Solve it and get your answers!