Two solutions of acid, one is 30% and one is 60%. How much of each solution do you need to mix to create 20 Liters of a new solution that is 42% acid?

Answer 1

x = number of liters at 30%

20 - x = number of liters at 60%

Compute a weighted combination of 30% and 60%:

(30%)x + (60%)(20 - x) = (42%)(20)

Can you solve for x and finish from here?

Answer 2

This problems asks for 2 equations to be solved at the same time:

(1.) Set x1 to be the volume of 0.30 concentrated acid and x2 to be the volume of 0.60 concentrated acid.

(2.) It is known that x1*0.3 + x2*0.6 = 20*0.42, where the end result is 20 liters of 0.42 concentrated acid.

(3.) We also know that x1 + x2 = 20 liters, as that is the final volume of acid the problem asks for.

(4.) The equations are found and can be set to be solved simultaneously:

(a.) x1*0.3 + x2*0.6 = 20*0.42

(b.) x1 + x2 = 20

Multiply row (b.) by -0.3 and add (b.) to (a.). This leaves x2 alone to be solved for a value of 8. Then take x2 = 8 value and use line (b.) to solve for x1.

This results in the solution to being x1 = 12

x2 = 8

Thus 12 liters of 0.30 concen. acid mixed in 8 liters of 0.60 concen. acid gets 20 liters of 0.42 concen. acid.