Algebra word problem

Question

How many liters of a 12% acid solution and a 20% acid solution should be mixed in order to obtain 4 liters of a 15% acid solution? 

Answer 1

Let x = amt. of 12% acid and y = amt. of 20% acid. Then we know that the mixture can be expressed as:

 

x + y = 4 or y = 4 - x

 

We also know that the total concentration needed for the mixture can be written as:

 

.12x + .20y = .15(4)

.12x + .20(4 - x) = 0.6 Now, let's multiply both sides of the equation by 100 to clear decimals. 

12x + 20(4 - x) = 60

12x + 80 - 20x = 60

80 - 8x = 60

-8x = -20

x = 20/8 = 5/2 = 2.5 L

 

To solve for y, we plug in for x:

 

y = 4 - x = 4 - 2.5 = 1.5 L