Answer:
Step-by-step explanation:
Let x be the number of gallons of 15% alcohol to be mixed and y be the number of gallons of 10% alcohol to be mixed.
We can set up the following system of equations based on the information given:
x + y = 5 (the total volume of the mixture is 5 gallons)
0.15x + 0.1y = 0.14(5) (the amount of pure alcohol in the mixture is 0.14 times the total volume of the mixture)
Simplifying the second equation, we get:
0.15x + 0.1y = 0.7
Multiplying both sides by 10 to eliminate the decimals, we get:
1.5x + y = 7
Now we can solve the system of equations by substitution or elimination to find x and y. Here, we will use the substitution method.
Solving the first equation for y, we get:
y = 5 - x
Substituting this expression for y into the second equation, we get:
1.5x + (5 - x) = 7
Simplifying and solving for x, we get:
0.5x = 2
x = 4
Substituting this value for x into the expression for y, we get:
y = 5 - 4 = 1
Therefore, we need 4 gallons of 15% alcohol and 1 gallon of 10% alcohol to obtain 5 gallons of 14% alcohol.