Question 250615
we have 100 gallons of 2% bleach


we need 100 gallon of 5% bleach.


100 * .02 = 2 gallons of bleach in the original mixture.


we need 100 * .05 = 5 gallons of bleach in the new mixture.


let x represent the number of gallons that have to be replaced.


we want to have 5 gallons in the new mixture.


we have 2 gallons in the original mixture.


we will need to add x gallons of pure bleach.


in the process we will be removing .02*x gallons of bleach from the original mixture.


the formula becomes:


5 = 2 - .02*x + x


where:


5 is the number of gallons of bleach we want in the new mixture.
2 is the number of gallons of bleach in the original mixture.
x is the number of gallons of pure bleach we will be adding.
.02*x is the number of gallons of pure bleach we will be removing.


the formula simplifies to:


5 = 2 + .98x


subtract 2 from both sides of this equation to get:


3 = .98x


divide both sides of this equation by .98 to get:


x = 3/.98 = 3.06122449


they need to replace 3.06122449 gallons of a 2% mixture with 3.06122449 gallons of pure bleach to reach the required concentration.


assume they remove 3.06122449 gallons of the 2% mixture.


they now have 96.93877551 gallons of 2% mixture.


this means they have .02 * 96.93877551 = 1.93877551 gallons of bleach.


they add 3.06122449 gallons of pure bleach.


their total gallons becomes 96.93877551 + 3.06122449 = 100 gallons.


their bleach content becomes 1.93877551 + 3.06122449 = 5 gallons.


they now have a 5% solution.


they needed to replace 3.06122449 gallons of the 2% mixture with 3.06122449 gallons of pure bleach.