SOLUTION: A chemist has one solution that is 25% alcohol and another that is 75% alcohol. How much of each must she use to make 14 liters of a solution that is 50% alcohol?

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Question 758135: A chemist has one solution that is 25% alcohol and another that is 75% alcohol. How much of each must she use to make 14 liters of a solution that is 50% alcohol?
Found 2 solutions by nerdybill, NSL1226:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
A chemist has one solution that is 25% alcohol and another that is 75% alcohol. How much of each must she use to make 14 liters of a solution that is 50% alcohol?
.
Let x = amount (liters) of 25%
then
14-x = amount (liters) of 75%
.
.25x + .75(14-x) = .50(14)
.25x + 10.5-.75x = 7
10.5-.50x = 7
-.50x = -3.5
x = 7 liters (25% alcohol)
.
amount of 75% alcohol:
14-x = 14-7 = 7 liters

Answer by NSL1226(3) (Show Source):
You can put this solution on YOUR website!
You're mixing an unknown volume of 25% solution with an unknown volume of a 75% solution to create a 14 liters of a 50% solution.
0.25x + 0.75x = 0.50 (14)

x = 7
so 0.25x = (0.25 * 7) = 1.75 liter
and 0.75x = (0.75 * 7) = 5.25 liter
This make 7 (1.75 + 5.25)liters of the correct solution, but we need 14 liters.
So, we simply double the amount of each, as follows:
2 * 1.75 Liter = 3.5 liter of the 25% solution, and
2 * 5.25 liter = 10.5 liter of the 75% solution.
Answer: 3.5 Liter of 25% solution and 10.5 liter of 75% solution.