Mom made a 5% bleach solution with 50 ml of bleach and 950 ml water. How much bleach should be added to this in order to obtain a 15% bleach solution?

1 Answer
Jun 6, 2018

117.6 ml

Explanation:

The current solution has 50 ml of bleach and a total volume of 50+950=1000 ml. If we add a certain quantity b of bleach, we will have more bleach, but also more solution in general: the ratio bleach-to-total volume will change as follows:

50+b1000+b

we want this ratio to equal 15%=0.15, so we must ask

50+b1000+b=0.15

Solve for b: if we multiply both sides by 1000+b we have

50+b=0.15(1000+b)=150+0.15b

Subtract 0.15b from both sides:

50+b0.15b=150

Subtract 50 from both sides:

b0.15b=15050

Simplify both sides:

0.85b=100

Divide both sides by 0.85

b=1000.85117.6

Let's check our answer: the new solution will have 50+117.6=167.6 ml of bleach, for a total volume of 1000+117.6=1117.6 ml. The ratio is

167.61117.60.15

so we're good!