A farmer has 100 gallons of 70% pure disinfectant. He wishes to mix it with the disinfectant which is 90% pure to obtain 75% pure disinfectant. How much of the 90% disinfectant must he use?

Apr 5, 2016

$33.3 \text{L}$

Explanation:

Amount of substance = concentration x volume

If $V$ is the volume of the 90% disinfectant then we can set up this equation:

$\left(100 \times 70\right) + \left(90 \times V\right) = 75 \left(100 + V\right)$

$\therefore 7000 + 90 V = 7500 + 75 V$

$\therefore 90 V - 75 V = 7500 - 7000$

$\therefore 15 V = 500$

$\therefore V = \frac{500}{15} = 33.33 \text{L}$