Question

A health clinic has a solution of bleach to sterilize petri dishes in which culture are grown. The sterilization tank contains 100 gal of a solution of 2% ordinary household bleach mixed with pure distilled water. Now research indicates that concentration of bleach should be 5% for complete sterilization. How much of the solution should be drained and replaced with bleach content to the recommended level?

Attempt:
Unfortunately, I have no idea as to how I will tackle this problem. This question is given for a pre-calculus course. Could anyone give me a hint as to how to approach this problem,

Answer 1

I must confess : I didn't really know how to tackle this problem, so I've "cheated" starting by the end :
You want to obtain a solution of 100 gal of a solution of 95% distilled water and 5% bleach, ie 95 gal of water and 5 gal of bleach. If you may drain only bleach, how many gal should you drain to obtain a solution with 98% water (our starting point).

The quantity of water remains the same as we only drain bleach : 95gal
\[95=\frac{98}{100}\times(100-x)\]
where x is the amoount of bleach drained, so :
\[x=100-\frac{95\times 100}{98}\approx 3.06 gal\]
You have then a solution of 96.94gal with 95gal of water (98%) and 1.94gal of bleach (2%)

So the answer is : you have to replace 3.06gal of your starting solution by bleach to obtain 100gal of a solution of 5%bleach.

I hope this may help you to start your problem ;)

Answer 2

In fact, according that you want 100gal of your final solution this could be a proper solution to your problem since 95 gal of water is precisely your goal.