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:1.25 galStep-by-step 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[tex]? =\frac{2.4(60-x)}{60}[/tex] 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 [tex]\frac{2.4(60-x)}{60}+x=3.6[/tex] Multiply both sides by 60 to eliminate the denominator [tex]2.4(60-x)+60x=60(3.6)[/tex] [tex]144-2.4x+60x=216[/tex] [tex]57.6x=72[/tex] [tex]x=\frac{72}{57.6}[/tex] [tex]\boxed{x=1.25 \;gal}[/tex]