Q:

A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 80 gal of a solution of 4% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 7% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?

Accepted Solution

A:
Answer:2.5 gal would have to be replaced with 100% bleach to get the right concentration.Step-by-step explanation:If we drain X gal from the tank and we replace it with X gal of 100% bleach we will have in the tank: 80-X gal of 4% bleach and X gal of 100% bleach.We can calculate the final concentration of the solution using a weighted average of the volumens where the weights are going to be the concentrations of each one:(7%)Γ—(80) = (4%)Γ—(80-X) + (100%)Γ—(X)560 = 320-4X+100X240 = 96XX=2.5 gal