SOLUTION: My algebra 2 question on my homework worksheet is this: "A health clinic uses a solution of bleach to sterilize Petri dishes in which cultures are grown. The sterilization tank

Click here to see ALL problems on Mixture Word Problems

Question 505697: My algebra 2 question on my homework worksheet is this:
"A health clinic uses a solution of bleach to sterilize Petri dishes in which cultures are grown. The sterilization tank contains 100 gal of a solution of 2% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 5% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?"
How would you solve that?
Found 2 solutions by ankor@dixie-net.com, oberobic:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A health clinic uses a solution of bleach to sterilize Petri dishes in which cultures are grown.
The sterilization tank contains 100 gal of a solution of 2% ordinary household bleach mixed with pure distilled water.
New research indicates that the concentration of bleach should be 5% for complete sterilization.
How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?"
:
Let x = amt of the 2% solution to be removed, and the amt of bleach to added
(Pure bleach would be 1x)
:
.02(100-x) + 1x = .05(100)
2 - .02x + 1x = 5
-.02x + 1x = 5 - 2
.98x = 3
x =
x ~ 3.06 gal of the 2% solution removed and 3.06 gal of pure bleach to be added
:
:
We can prove that
.02(100-3.06) + 3.06 = .05(100)
.02(96.94) + 3.06 = 5
1.9388 + 3.06 = 4.9988 ~ 5

Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
With mixture problems you always have to keep track of how much 'pure' stuff you have.
.
At present you have 100 gal of 2% solution.
2%(100) = .02*100 = 2 gallons of pure bleach added to 98 gallons of water.
.
What you need is 5 gallons of bleach added to 95 gallons of water.
But you cannot do that because you have a tank full.
So, you have to drain the same amount of solution as you add.
.
Let 'x' be the amount you add, which = the amount you drain.
.
2%(100) + 100%(x) - 2%(x) = 5%(100)
.
.02(100) + 1(x) - .02(x) = .05(100)
.
2 + x - .02x = 5
.
.98x = 3
.
98x = 300
.
x = 300/98
.
x = 3.0612
.
Always check your solution to see if it is truly the answer.
.
You plan to drain 3.06 gallons of the 2% solution and add 3.06 gallons of pure bleach.
.
Would that be a 5% solution?
.
The amount you drain would take some of the pure stuff with it.
.
.02*(3.0612) = .0612 gal of pure stuff would be removed from the 2.0 gallons you had in total.
.
So you would still have 1.9388 gal of pure stuff in the tank.
.
Then you add 3.0612 gallons of pure stuff, which fills the tank again.
.
1.9388 + 3.0612 = 5 gallons of pure stuff in the 100 gal tank.
That's a 5% solution.
.
Answer:
Drain 3.0612 of 2% solution from the 100 gallon tank and add 3.0612 gallons of pure bleach to produce 100 gallons of 5% solution.
.
Done.