Question

A health 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?

Answer 1

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.