Answer:
Explanation:
Let x be the number of gallons of 15% alcohol needed.
Then the number of gallons of 10% alcohol needed is 5 - x.
The amount of pure alcohol in x gallons of 15% alcohol is 0.15x, and the amount of pure alcohol in 5 - x gallons of 10% alcohol is 0.1(5 - x).
To obtain 5 gallons of 11% alcohol, the amount of pure alcohol in the mixture must be:
0.11(5) = 0.15x + 0.1(5 - x)
Simplifying and solving for x, we get:
0.55 = 0.05x + 0.5 - 0.1x
0.55 = 0.5 - 0.05x
0.05x = 0.05
x = 1
Therefore, we need 1 gallon of 15% alcohol and 4 gallons of 10% alcohol to obtain 5 gallons of 11% alcohol.
To answer the additional questions:
The mixture contains 1 gallon of 15% alcohol.
The mixture contains 4 gallons of 10% alcohol.