Ahealth clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. the sterilization tank contains 90 gal of a solution of 4% ordinary household bleach mixed with pure distilled water. new research indicates that the concentration of bleach should be 8% for complete sterilization. how much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?

3.75 gallons need to be drained and replaced with bleach. Change the problem to "What amounts of a 100% solution and a 4% solution is needed to make 90 gallons of a 8% solution?" Given that, we'll use the following values. x = amount of 4% solution. 90-x = amount of a 100% solution. The equation to solve then becomes. 0.04 x + (90-x) = 0.08 * 90 0.04 x + 90 - x = 7.2 Add x to both sides 0.04x + 90 = 7.2 + x Subtract 0.04x from both sides 90 = 7.2 + 0.96x Subtract 7.2 from both sides 82.8 = 0.96x Divide both sides by 0.96 86.25 = x So you now know that you need 86.25 gallons of the original 4% solution and (90-86.25) = 3.75 gallons of the bleach to make the desired 90 gallons. So simply drain 3.75 gallons from the tank and replace with bleach.

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