system of equations: total value and Mixtur Problems

Question

etch clean graghics  use some clenser that is 25% acid and a secound that is 50% acid. How many liters of each should be mixed to get 30L of a solution that is 40% acid?

Answer 1

Let T = liters of 25% acid

Let F = liters of 50% acid

 

We want 30L total  ==>  T + F = 30  ==> F = 30 - T

 

We want the final solution to be 30L that is 40% acid  ==>  

it contains 30L * 0.40 = 12L acid 

 

The total amount of acid in the mixture of T liters of 25% acid and F liters of 50% acid is given by 0.25T + 0.50F

 

So our 2nd equation is 0.25T + 0.50F = 12

 

Substitute the value for F from the 1st equation in to this equation and solve for T

 

0.25T + 0.50(30 - T) = 12

0.25T + 15 - 0.50T = 12

-.25T = -3

T = 12

 

So F = 30 - T = 18

 

We should mix 12 liters of 25% acid with 18 liters of 50% acid 

 

Check:  12L + 18L = 30L total

            0.25(12) + 0.50(18) = 3 + 9 = 12L acid in mixture so mixture is 12/30 = 40% acid