Is a tub contains 50 pounds of a 5% solution of brine, how much water myst evaporate to change it to an 8% solution

Question

Math 

Answer 1

The fraction the percentages represent are important.  We start with a mixture that is 95% water (5% salt), remove an unknown amount of 100% water (zero % salt) and end up with a mixture that is 92% water (8% salt).

 

(50 lbs)(.95) - (x lbs)(1) = (50 - x)(.92)

 

50(.95) - x = (50 - x)(.92)

 

Multiply by 100 to clear the fractions.

 

50(95) - 100x = (50 - x)(92)

 

Simplify.

 

4750 - 100x = 4600 - 92x

 

150 = 8x

 

x = 18.75

 

18.75 pounds of water have to evaporate to change the solution to 8% brine.