linear equation

Question

A scientist needs 90 liters of a 50% acid solution. He currently has 30% solution and 60% solution. How many liters of each does he need to make the needed 90 liters of 50% acid solution

 

A scientist needs __ liters of 30% solution (type and integer or decimal)

Answer 1

Let x = liters of 30% solution and let 90 - x = liters of 60% solution (since eventually he wants 90 liters of solution).

 

The amount of acid in the 30% solution is 0.3x, while the amount of acid in the 60% solution is 0.6(90 - x) = 54 - 0.6x.

 

90 liters of a 50% acid solution must contain 0.5(90) = 45 liters of acid. So:

 

(acid in first solution) + (acid in second solution) = (acid in third solution)

0.3x + (54 - 0.6x) = 45

0.3x + 54 - 0.6x = 45

-0.3x + 54 = 45

-0.3x = -9

x = 30

 

The scientist needs x = 30 liters of 30% solution.