Question

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 6% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level? 4.5425 x gal Need Help? Read It Talk to a Tutor Page 1 of 1 0 Words English (US) E E. ' - - - + 288%

Answer 1

1.25 gal

Explanation:

4% of 60 equals 2.4, that means the tank contains 2.4 gal of pure bleach.

You want the tank to contain 3.6 gal of pure bleach because 6% of 60 equals 3.6.

Now suppose you drain x gallons of solution, so now you 60-x gal in the tank.

In order to know how much bleach the tank has now, cross multiply

60 gall --------------> 2.4 gal pure bleach

60-x ------------------> ?

so

`? =(2.4(60-x))/(60)`

Now, you want to add x gal of pure bleach to complete the solution extracted in such a way that the amount of pure bleach in the tank is now 3.6, so we get the linear equation

`(2.4(60-x))/(60)+x=3.6`

Multiply both sides by 60 to eliminate the denominator

`2.4(60-x)+60x=60(3.6)`

`144-2.4x+60x=216`

`57.6x=72`

`x=(72)/(57.6)`

`\boxed{x=1.25 \;gal}`