Question

A pot contains 6L of brine at a concentration of 120g/L. How much of the water should be boiled off to increase the concentration to 200g/L?

Short answer

2.4 L of water should be boiled.

Step-by-step solution

Step-1. Setup the model.

Let x be the amount of water should be boiled.

Thus,$6-x$ will be the remaining water.

Also, the total concentration of 6L brine is$6\times 120=720\text{g}$

Since the amount of brine remains the same but concentration increases thus,

$6\times 120=(6-x)\times 200$

Step-2. Isolate the variable.

$\begin{array}{l}6\times 120=(6-x)\times 200\\ 720=1200-200x\\ 200x=1200-720\\ 200x=480\end{array}$

Step-3. Solve of x.

$\begin{array}{l}x=\frac{480}{200}\\ x=2.4\end{array}$

Hence, 2.4L of water should be boiled.