Dilute a 70% solution in a 55 gallon drum to 10%.

Question

I have a 55 gallon drum that contains a 70% detergent solution. If I want to dilute that solution to 10%, how much water do I add?

Answer 1

55 Gallons at 70% has $55 \times 0.7 = 38.5$

$38.5 = 10%$ so the full amount of liquid is 385 gallons

therefore you need to add $385 - 55$ gallons of water $= 330$

Answer 2

Let $d$ = amount of detergent, $w$ = original amount of water, and $x$ = amount of water to add.

$$w+d=55$$

The solution contains $70\%$ detergent and $30\%$ water. Therefore: $$w=0.3 \cdot 55 = 16.5$$

Now, let's add $x$ water. The total amount of water is now $w+x$ and the whole solution $55+x$.

A $10\%$ detergent concentation means $90\%$ is water:

$$w+x = 0.9 \cdot (55+x)$$ $$\Rightarrow x=330$$