Question 1184883
<br>
You have received responses showing three different algebraic solutions -- one using three variables, one using two, and one using one.<br>
Use the solution from the tutor who uses one variable.  Taking the little extra time to figure out how to set up the problem using a single variable will save you a lot of time in solving the problem.<br>
Here then is a completely different method for solving this kind of problem, without formal algebra.  The words of explanation make it sound long and difficult; but the calculations are relatively simple, so if your mental math is good you can solve the problem quickly by this method.<br>
First consider mixing the 40% and 85% acid, using twice as much of the 85% acid.  That means 2/3 of this mixture will be the 85% acid; and that means the percentage of this mixture will be 2/3 of the way from 40% to 85% -- which is 70%.<br>
Then consider mixing this 70% acid solution with the 25% acid solution to get a 35% acid solution.  35% is (35-25)/(70-25)=10/45=2/9 of the way from 25% to 70%, so 2/9 of the 135 liters total, or 30 liters, is the 70% acid solution.<br>
Then, since the 70% acid solution contains twice as much 85% acid as 40% acid, the mixture contains 10 liters of 40% acid and 20 liters of 85% acid.<br>
Then the amount of 25% acid solution used in the mixture is 135-30=105 liters.<br>
ANSWERS:
25%: 105 liters
40%: 10 liters
85%: 20 liters<br>
CHECK:
.25(105)+.40(10)+.85(20)=26.25+4+17=47.25
.35(135)=47.25<br>