SOLUTION: The sterilization tank contains 100 gallons of a solution of 2% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach

Question 250615: The sterilization tank contains 100 gallons of a solution of 2% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 5% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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