SOLUTION: how much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get an 80% acid solution

Question 243494: how much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get an 80% acid solution
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Always start by sorting out what you know and assigning variables. We know we have 9 gallons of 50% acid solution. Multiplying 9 by .5 = 4.5 gallons of pure acid in the solution.
.
We need to know how much more pure acid we need to add to get an 80% acid solution.
.
Set the unknown to x.
.
Since we are adding x gallons of pure acid, the final solution will be 9+x gallons at 80% acid. We can state this algebraically as: .8(9+x)
.
It will consist of 9 gallows of .5 acid solution + x gallons of 100% acid. We can show this as
.5(9) + 1(x)
.
Of course, we don't normally show 1 times anything. But I just wanted to be clear.
.
Combining we have:
.8(9+x) = .5(9) + x
Multiplying what we have in parentheses
7.2 + .8x = 4.5 + x
Subtracting 4.5 from both sides
2.7 + .8x = x
Subtracting .8x from both sides
2.7 = .2x
Dividing both sides by .2
13.5 = x
x = 13.5
.
So this suggests we need to add 13.5 gallons of pure acid to get to an 80% solution.
That seems like an awful lot. But we always check our work, so that's next anyway.
.
If we add 13.5 gallons to 9 gallons, we have 22.5 gallons of solution in total.
If it is 80% acid, then we would have .8(22.5) = 18 gallons of pure acid in the solution.
We started with 4.5 gallons of pure acid and added 13.5 gallons of pure acid = 18.
Done.
RELATED QUESTIONS
How much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get... (answered by CharlesG2)

how much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get... (answered by mananth)

How much pure acid should be mixed with 2 gallons of a 50% acid solution in order to get... (answered by checkley75)

How much pure acid should be mixed with 2 gallons of a 50% acid solution in order to get... (answered by checkley77)

how much pure acid should be mixed with 5 gallons of a 50% acid solution in order to get... (answered by ewatrrr)

How much pure acid should be mixed with 8 gallons of a 50% acid solution in order to get... (answered by josmiceli)

How much pure acid should be mixed with 4 gallons of a 50% acid solution in order to get... (answered by josgarithmetic)

How much pure acid should be mixed with 7 gallons of a 50% acid solution in order... (answered by ankor@dixie-net.com)

how much pure acid should be mixed with 4 gallons of a 60% acid solution in order to get... (answered by robertb)