How much water must be added to 20 L of a 10% solution of boric acid to reduce it to a 4% solution?

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Answer 1 · 2015-08-13T10:13:41

You have to add 30 litres of water

At the beginning you have 20 L of 10% solution, so it consists of 2L of acid and 18 L of water.

Now you have to calculate the amount of water to add to change the solution to 4%.
To do this you have to solve equation:

$\frac{2}{20 + x} = \frac{4}{100}$ $2/(20+x)=4/100$

The equation comes from the fact that the amount of acid is unchanged (2L) and the sum of water and acid is increased by $x$ $x$ (added water)

$\frac{2}{20 + x} = \frac{2}{50}$ $2/(20+x)=2/50$

$40 + 2 x = 100$ $40+2x=100$

$2 x = 100 - 40$ $2x=100-40$
$2 x = 60$ $2x=60$
$x = 30$ $x=30$