SOLUTION: How many gallons of hydrochloride acid must be added to 12 gallons of a 30% solution to obtain a 40% solution?

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Question 776256: How many gallons of hydrochloride acid must be added to 12 gallons of a 30% solution to obtain a 40% solution?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What is the concentration of the Hydrochloric Acid to add? That datum is necessary. Otherwise, we have an extra variable with no given value.

Let h = concentration of your concentrated hydrochloric acid
L = 30% HCl
T = 40% HCl
U = 12 gallons of the 30%
v = volume gallons of the concentrated hydrochloric acid HCl still of unknown value

You do not know nor need the expected amount of volume of the 40% target concentration, or if so, it is not part of this problem.

Equation for the mixing is this:
%28LU%2Bhv%29%2F%28U%2Bv%29=T
You can solve the equation for v but you cannot get a value for it until you have a value for h.