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?

What are you being asked to find in this problem?

gallons of pure water

gallons of 12% salt solution

gallons of 20% salt solution

The correct answer option is: 'gallons of pure water'.

Step-by-step explanation:

We are asked to find the number of gallons of pure water in this problem.

We know that the amount of salt that exists in the solution before the pure water is evaporated (0.12) (160) has to be equal to the amount of salt which is there after the evaporation takes place (0.20) (160-x).

Therefore, the number of gallons of pure water can be found using this equation:

(0.12) (160) = (0.20) (160-x)

Answer: It is asking the amount of pure water.

Amount of pure water evaporated is 64 gallons.

Step-by-step explanation:

Let x gallons be the amount of evaporated water.

Amount of water before evaporation

=12% of 160

= 0.12 (160) = 19.2 gallons ... (1)

amount of solution after x gallon water evaporation = 160-x

amount of salt in 160-x solution = 20% of 160-x

=0.2 (160-x) ... (2)

Since amount of salt will be same before and after evaporation

from (1) and (2)

0.2 (160-x) = 19.2

32-0.2x = 19.2

-0.2x = 19.2-32

-0.2x = - 12.8

x = - 12.8 / (-0.2)

x = 64 gallons