MIXING TWO SOLUTIONS
PROBLEM
Usually you are given:
1) the percent strength of each solution
2) the total volume
Problem: Solution X is 60% acid. Solution Y is 30% acid. How much of EACH solution is needed to make 180 liters of a solution that is 40% acid?
Solution: Let X represent the liters of solution X and Y represent the liters of solution Y.
Write a system of equations:
Strength equation: 60%X + 30%Y = 40%(180)
or .60X + .30Y = .40(180)
or .60X + . 30Y = 72
Volume equation: X + Y = 30
Now solve the system of your two equations:
Because 30% is the smallest percent, we’ll eliminate it by multiplying the volume equation by 30% = .30 in order to obtain opposites:
(.30)X + (.30)Y = (.30)180
or .30X  .30Y = 54
Now rewrite the system in order to solve it:
.60X + .30Y = 72
.30X  .30Y = 54
.30X = 18
Divide BOTH sides by .30:
.30X = 18
.30 . 30
X = 60 liters of solution X which has a strength of 60% acid.
If the container holds 180 liters, subtract to find the volume of solution Y:
180 – 60 = 120 liters of solution Y which has a strength of 30% acid.
