Solve Mixture Problems

Question

A chemist needs 8 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How much of each of the two solutions should she mix to obtain her desired solution?

 

 

 

 

 

 

 

 

( the answer is 3.2 liters of the 20% solution; 4.8 liters of the 70% solution. I need help on how they got this answer) 

Answer 1

Cathyrin, this problem can be set up as a system of two equations with two unknowns.

 

Let x=the amount of 20% solution

Let y=the amount of 70% solution

 

x+y=8 This equation is based upon the total amount of the 50% solution being equal to 8 liters.

This implies y=8-x

 

0.2x+0.7(8-x)=0.5(8)=4 Multiply the equation by 10 to simplify the arithmetic. 

 

2x+7(8-x)=40

2x+56-7x=40

-5x+56=40

     -56  -56

       -5x=-16  Divide both sides by -6

 

          x=3 1/5 =3.2

          y=8-3.2=4.8

 

Hence, you would need to combine 3.2 liters of 20% and 4.8 liters of 70% solutions to get 8 liters of 50% solution.