# How much pure acid should be mixed with 5 gallons of a 20% acid solution in order to get a 50% acid solution?

Nov 17, 2016

3 gallons

#### Explanation:

So we know that we're adding pure acid, so that would be 100%. We don't know how much pure acid we're adding, so we'll designate $x$ to represent that quantity. Forming the equation, we get
$1.00 x + 0.20 \left(5\right) = 0.50 \left(x + 5\right)$
Simplifying, we get
$x + 1 = 0.5 x + 2.5$
$x - 0.5 x = 2.5 - 1$
$0.5 x = 1.5$
$x = 3$
So we need 3 gallons of pure acid.