A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 60 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

2.5 gallons that are removed and 2.5 gallons of bleach that are added

Explanation:

Let's take as

x = amount of the original solution that is removed and the amount of bleach to add.

The equation for the amount of lye is equal to:

0.04*(60 - x) + x = 0.08*(60)

2.4 - 0.04x + x = 4.8

-0.04x + x = 4.8 - 2.4

0.96x = 2.4

Clearing x:

x = 2.4/0.96

x = 2.5 gallons that are removed and 2.5 gallons of bleach that are added

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