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.