How many liters of each solution should be used?

Question

A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 40% and the third contains 60%. He wants to use all three solutions to obtain a mixture of 120 liters containing 35% acid, using 3 times as much of the 60% solution as the 40% solution. How many liters of each solution should be used?

Answer 1

Let x = #L of 25%

Let y = #L of 40%

Let 3y = #L of 60%

 

VOLUME EQUATION:  x + y + 3y = 120, so x + 4y = 120  (a)

 

CONCENTRATION EQUATION: 0.25x + 0.40y + 0.60(3y) = 0.35*120

 

   Simplifying this, we get:  0.25x + 2.2y = 42 (b)

 

Multiply (b)*4:    x + 8.8y = 168

subtract (a):       x + 4y    = 120

                               4.8y = 48

                                    y = 10 L  of 40% acid

                                  3y = 30 L  of 60% acid

 x + 4(10) = 120,    so  x  = 80 L  of 25% acid