SOLUTION: Solution A is 30% acid and solution B is 50% acid. How much of each should be used to make 120 liters of a solution that is 40% acid?

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Question 747109: Solution A is 30% acid and solution B is 50% acid. How much of each should be used to make 120 liters of a solution that is 40% acid?
Found 2 solutions by josgarithmetic, mikeebsc:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The values are picked so that the quantities can be found through intuition and logic. 40% is exactly in the middle of 30% and 50%. For 120 liters mixture, the quantity of each starting solution is 60 liters each.

ANSWER: 60 liters of each.


ARITHMETIC:
let u = liters of 30%
let v = liters of 50%
%2830u%2B50v%29%2F%28120%29=40 and u%2Bv=120
Find u and v.





You can begin simplifying the rational equation by dividing both sides by 10 and have %283u%2B5v%29%2F120=4.

Answer by mikeebsc(26) About Me  (Show Source):
You can put this solution on YOUR website!
Because this is a relatively simple one, we can just use a little logic to solve it.
A 40% solution is directly in the middle of the 30% and 50% solution, so equal amounts of each will be used, so just divide 120(total liters needed)/2(number of solutions available)
120/2=60
You will need 60 liters of the 30% and 60 liters of the 50% solution to equal 120 liters of 40% solution.
Harder problems will require more in depth arithmetic, but for this problem, this is enough.