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
total solution	a

what is the original amount of solution in gallons? a =

Explanation:

Step1: 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. The original amount of solution $a = 160$ gallons.

Step2: Let $x$ be the amount of water 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: $19.2=0.2\times(160 - x)$.
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