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
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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?
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.
