Answer:
300 gallons
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