Solve How many ounces of alcohol are in 40oz of a 5 alcohol

Solve: How many ounces of alcohol are in 40oz of a 5% alcohol solution? How many liters of a 40% antifreeze solution must be mixed with 51 of a 70% antifreeze solution to make a 12% alcohol solution?

Solution

a) The number of ounces of alcohol in 40oz of 5 % alcohol is 5/100(40) = 2 oz.

b) Let x liters of 40% antifreeze solution be mixed with 5 liters of 70% antifreeze solution to make 12% alcohol solution. Then the total volume of 12% alcohol solution is x +5 liters. The quantity of alcohol in this solution is (40/100)x + (70/100)*5 = 0.4x +3.5 liters. Since the solution is 12 % alcohol, hence (12/100)(x+5)= 0.4x +3.5 or, 0.12x + 0.6 = 0.4x +3.5 or, 0.4x -0.12x = 0.6-3.5 or, 0.28x = - -2.9 or x = -2.9/0.28 = -10.36 which is apparently incorrect. Even otherwise, is any quantity of 40 % antifreeze solution is mixed with any quantity of 70 % antifreeze solution, then the resultant solution will be between 40% and 70 % alcohol concentration. It cannot be 12% alcohol concentration.