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?

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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?

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Answer 1 · 2018-06-06T16:11:17

$117.6$ $117.6$ ml

Explanation:

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

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

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

$\frac{50 + b}{1000 + b} = 0.15$ $\frac{50+b}{1000+b} = 0.15$

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

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

Subtract $0.15 b$ $0.15b$ from both sides:

$50 + b - 0.15 b = 150$ $50+b-0.15b = 150$

Subtract $50$ $50$ from both sides:

$b - 0.15 b = 150 - 50$ $b-0.15b = 150 - 50$

Simplify both sides:

$0.85 b = 100$ $0.85b = 100$

Divide both sides by $0.85$ $0.85$

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

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

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

so we're good!

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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

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