How much pure acid should be mixed with 6 gallons of a 60% acid solution in order to get an 80% acid solution?

Question

anonymous · Answer

I really need help!!

ganeshie8 · Answer

To start with, you have 6 gallons of a 60% acid solution. 

Whats 60% of 6 gallons ?

anonymous · Answer

3.6?

ganeshie8 · Answer

Yes, so we have 3.6 gallons of acid in the given 6 gallon solution

ganeshie8 · Answer

Lets pour some pure acid and increase the concentration to 80%

ganeshie8 · Answer

As usual, let $x$ be the amount of extra acid that we need to pour to increase the concentration to 80%

ganeshie8 · Answer

Then in the end, we will be having $x+3.6$ gallons of pure acid in the $x+6$ gallon solution, yes ?

ganeshie8 · Answer

We want the acid in this final solution to be 80% :

$$x+3.6 = \text{80% of }(x+6)$$

ganeshie8 · Answer

$$x+3.6 = 0.8(x+6)$$

you can solve $x$

anonymous · Answer

Okay, wait, i'm about to do it.

ganeshie8 · Answer

Okay, take your time

anonymous · Answer

I got 6.

ganeshie8 · Answer

Correct!

anonymous · Answer

Thanks a lot!!

ganeshie8 · Answer

So, the final solution will have 6+3.6 = 9.6 gallons of acid
And the solution would be 6+6 = 12 gallons

ganeshie8 · Answer

To verify your answer, you may simply find how much percent 9.6 is  of 12

ganeshie8 · Answer

you should get 80%