Question

Solution X is 30% alcohol and solution Y is 60% alcohol. How much of each should be used to make 300 liters of a 40% solution.

Answer 1

what is 40% of 300?

Answer 2

Mixture problems are often easier if you think in terms of the amount of the ingredient of interest. In this one, you want to make 300 l of a 40% solution, which means there will be a total of 40% * 300 l = 0.4*300 l = 120 l of alcohol in the final product. So, the trick is to find out how many liters of solution X and solution Y must be combined to produce 120 l of alcohol in 300 l of solution.

let X be the number of liters of solution X, and Y be the same for solution Y.

We know that we are making 300 l of solution, so X+Y = 300 is our first equation. Our second equation will be 30% * X + 60% * Y = 40% * 300

Solve those and you have your answer.

Answer 3

\[.3x+.6(300-x)=120\] is a start, since \(.4\times 300=120\)

Answer 4

@satellite73's setup is the other typical way to do this sort of thing — it does the substitution method to solve the equations while you are setting it up. If there are only two quantities involved, it's a little easier; if you're mixing more things, then the extra steps in my approach can be easier to understand. Both approaches give the same answer, barring mistakes.