Turtle S.

asked • 07/10/15# Construction of Equation when working with mixture problems

"Brine is a solution of salt and water. If a tub contains 50 gallons of a 5% solution of brine, how much water must evaporate to change it to an 8% solution? " Is the problem I'm working with but I'm having trouble understanding how to construct an equation can I get some help please? Do I use subtraction (0.08(50-x)) I'm really lost and help would be appreciated. Thank you

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## 2 Answers By Expert Tutors

Peter C. answered • 07/10/15

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50(0.05) = 0.08(50-x) x = gallons to be evaporated

5/2 = 4 - 0.08x

5/2 -4 = -0.08x

8/2- 5/2 = 0.08x

3/(2(.08)) = x = 18.75

Jayden H. answered • 07/10/15

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I will leave my initial first paragraph up here so that the comment below makes sense. My understand of the characteristics of Brine are flawed. Mass is conserved but not volume. Thank you for clearing this up LeVar.

Please follow Peters solution.

"You have 50 gallons of solution. 5% of the solution is salt and 95% is water. How much water must be separated and taken out of the solution so that there is 8% salt and 92% water. The amount of salt in the tub is constant throughout the whole question."

LeVar D.

The final equation used to solve the problem works perfectly, but I believe the salt and water percentage breakdown works differently than explained in the first paragraph. For the 50 gallons of 5% brine solution, I believe the 50 gallons is made up of salt dissolved into 50 gallons of water as opposed to 2.5 gal of salt added to 47.5 gal of water for a total volume of 50 gallons (the 5% salt/ 95% water breakdown). When adding the salt to the water, the initial combined volume will increase until the salt is dissolved at which point the total volume will return to roughly the amount of water you started with (well, actually slightly less).

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07/10/15

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Jayden H.

07/10/15