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?

Question

Mathematics

Gunner Weiss

20 April, 12:39

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?

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Cade Hawkins · Answer 1

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%) * (80) = (4%) * (80-X) + (100%) * (X)

560 = 320-4X+100X

240 = 96X

X=2.5 gal