A chemist needs 88 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

Question

A chemist needs 88 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?

Answer 1

s represents the amount of 70% solution

88 - s represents the amount of 20% solution

0.2(88 - s) + 0.7s = 0.5(88)

 

Can you solve for s and answer the question?

Answer 2

Hello Liz.

 

Let's say we will mix x liters of 20% salt solution and y liters of 70% salt solution:

 

20% salt solution: x liters

70% salt solution: y liters

 

We want 88 liters, so x + y = 88 liters.

 

Now, the salt concentration of the mixture will be (0.20x + 0.70y)/(x + y),

and we want this to equal 50% or 0.50. So:

 

0.20x + 0.70y =0.5(x + y) --> 0.3x = 0.2y --> y = 1.5x.

 

Substitute y = 1.5x to get:

 

x + y = x + 1.5x =2.5x =88.

 

x = 35.2 liters

y = 52.8 liters.