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Your question consists of ratios.
.5(6)/6= 3/6 3 is the gallons of acid. 6 is the total gallons
To find out how much more gallons of acid you need to obtain 80% acid levels we add our unknown amount to bottom and top of the ratio indicating for the top more acid gallons and for the bottom more total gallons overall.
3+x/6+x= .8
Solve for 'x'
The format for this type of problem is to figure out your initial amounts then set up a ratio equaling the new desired percentage. You must be sure of how the information is applied in the problem for instance had we been adding non-acid solution then there would be no 'x' variable on the top since the ratio we have is acid gallons/ total gallons. Adding non-acid does not apply to acid. Good tip is to visualize the problem in your mind (if it's possible don't get brain freeze however)

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Here's the problem restated:
Step 1. Isolate the variable by it's self

on the left hand side the two "19"'s cancel becoming...

"4-19" equals "-15" so rewriting

Step 2. Reverse whatever process is being done to "x" if "x" is being multiplied, you divide, if it's being divided, you multiply. etc

multiply both sides by two

The left hand side with "x" is being divided by "2" and multiplied by "2" these effects cancel each other out.

multiply the right hand side

To check our answer we input the solution we concluded which was "-30" into the original problem which was




Since we arrived at a mathematical truth (that "4" is indeed "4") the solution we concluded is indeed correct. It's my wish that you will be able to understand any type of problem of this manner. Please let me know if you have any further questions regarding this problem or any other math problem that's a puzzler for you.

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Correct.