Question

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?

Answer 1

`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:

`\frac{50+b}{1000+b}`

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

`\frac{50+b}{1000+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+b-0.15b = 150`

Subtract `50` from both sides:

`b-0.15b = 150 - 50`

Simplify both sides:

`0.85b = 100`

Divide both sides by `0.85`

`b = \frac{100}{0.85} \approx 117.6`

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

`\frac{167.6}{1117.6} \approx 0.15`

so we're good!