Answers

1. Answer:

   300 gallons

   Step-by-step explanation:

   A saline solution is a solution of salt in water.

   The percent is the percent of salt in the total amount of solution.

   A 40% saline solution has 40% of salt out of the total volume.

   Let the amount of pure water needed = x.

   The amount of existing 40% solution is 500 gal.

   Let the total amount of 25% saline solution made = y.

   Equation of volumes of solutions:

   500 + x = y

   y = x + 500          Eq. 1

   Equation of volume of salt:

   500 gal of 40% saline solution has 0.4 × 500 gal = 200 gal of salt

   Pure water has 0% salt.

   The final product is a solution that is 25% saline. Its volume is y.

   The volume of salt in the y gallons of 25% saline solution is 25% of y = 0.25y

   The equation of salt content is:

   200 + 0 = 0.25y

   y = 800       Eq. 2

   Eq. 1 and Eq. 2 form a system of equations.

   y = x + 500

   y = 800

   Substitute 800 for y in Eq. 1.

   y = x + 500

   800 = x + 500

   x = 300

   Answer: 300 gallons of pure water

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