How many gallons of pure water must be added to 500 gallons of a 40% saline solution to reduce it to 25% saline solution
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Answer:300 gallonsStep-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 = yy = x + 500 Eq. 1Equation of volume of salt:500 gal of 40% saline solution has 0.4 × 500 gal = 200 gal of saltPure 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 = 0.25yThe equation of salt content is:200 + 0 = 0.25yy = 800 Eq. 2Eq. 1 and Eq. 2 form a system of equations.y = x + 500y = 800Substitute 800 for y in Eq. 1.y = x + 500800 = x + 500x = 300Answer: 300 gallons of pure water