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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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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%)×(80) = (4%)×(80-X) + (100%)×(X)

560 = 320-4X+100X

240 = 96X

X=2.5 gal