Question

how many gallons of pure water should be evaporated from 160 gallons of a solution containing 12% salt so that the remaining solution contains 20% salt?

Explanation:

Step1: Find the amount of salt

The initial solution is 160 gallons and contains 12% salt. So the amount of salt is $160\times0.12 = 19.2$ gallons.

Step2: Let the amount of water to be evaporated be $x$ gallons

The new - volume of the solution is $(160 - x)$ gallons, and the amount of salt remains the same. We want the new solution to be 20% salt. So we can set up the equation: $\frac{19.2}{160 - x}=0.2$.

Step3: Solve the equation for $x$

Cross - multiply the equation $\frac{19.2}{160 - x}=0.2$ to get $19.2 = 0.2\times(160 - x)$.
Expand the right - hand side: $19.2=32−0.2x$.
Add $0.2x$ to both sides: $0.2x + 19.2=32$.
Subtract 19.2 from both sides: $0.2x=32 - 19.2=12.8$.
Divide both sides by 0.2: $x=\frac{12.8}{0.2}=64$.

Answer:

64 gallons