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? fill in the table: original removed new amount of salt b total solution a what is the original amount of solution in gallons? a = done

Explanation:

Step1: Find original amount of solution

The problem states the original amount of solution is 160 gallons. So $a = 160$.

Step2: Find original amount of salt

The original solution is 160 gallons and contains 12% salt. So the amount of salt $b=160\times0.12 = 19.2$ gallons.
Let $x$ be the amount of water (in gallons) to be evaporated.
The new - total amount of solution is $160 - x$ gallons, and the amount of salt remains the same (19.2 gallons).
We know that the new solution is 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: $0.2x=32 - 19.2$.
$0.2x = 12.8$.
Divide both sides by 0.2: $x=\frac{12.8}{0.2}=64$.

Answer:

64