Answer:
C. 18.75 gallons
Step-by-step explanation:
Given,
Total solution = 50 gallons,
The quantity of brine in the solution = 5 % of 50 = 2.5 gallons,
And, the original quantity of water in the solution = Total solution - Brine
= 50 - 2.5 = 47.5 gallon,
Let x be the quantity of water that must evaporate to change it to an 8% solution,
Also, the ratio of the brine and water in the resultant solution = 8 : 92
So, we can write,
[tex]\frac{2.5}{47.5-x}=\frac{8}{92}[/tex]
[tex]230=380-8x[/tex] ( By cross multiplication )
[tex]8x = 380 - 230 = 150[/tex]
[tex]\implies x = \frac{150}{8}=18.75[/tex]
Hence, 18.75 gallons of water must evaporate to change the percentage of brine from 5 % an 8 %.
Option C is correct.
