SOLUTION: Glenn is a chemist with Gemco Pharmaceutical. He needs to prepare 40 gallons of a 15% hydrochloric acid solution find the amount of a 12% solution and the amount of a 20% solution

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Question 738782: Glenn is a chemist with Gemco Pharmaceutical. He needs to prepare 40 gallons of a 15% hydrochloric acid solution find the amount of a 12% solution and the amount of a 20% solution he should mix to get this solution.
Again, i know how to solve a system of equations, but i dont know how to translate this problem, please help.
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = gallons of 12% solution needed
Let = gallons of 20% solution needed
--------------
(1)
(2)
----------------------------
(2)
(2)
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)

and, since
(1)
(1)
25 gallons of 12% solution are needed
15 gallons of 20% solution are needed
check:
(2)
(2)
(2)
OK

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Myself, I wouldn't go to all of the trouble to set up a system of equations for this one. I would do it this way:

Then I would solve for and calculate .

However, this is just two steps in to solving the following two-variable system by substitution:

Note that I didn't need to use decimal fractions because the second equation and this one:

are equivalent.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it