Answer:
The amount of gallons of 20% of moonshine required = 50gallons
The amount of gallons of 30% of moonshine required = 50gallons
Explanation:
We need to determine the amount of gallons of 20% of moonshine and amount of 30% of moonshine that is required to make 100gallons of 25% moonshine mixture
x = amount of gallons of 20% moonshine
y = amount of gallons of 30% moonshine
x(20% of moonshine) + y(30% of moonshine) = 100(25% of moonshine)
0.2x + 0.3y = 100(0.25)
0.2x + 0.3y = 25 ...equation (1)
Also the addition of the amount of each concentration = amount of mixtures
x + y = 100 ....equation (2)
Using elimination method:
Multiply equation 2 by 0.2 in order to eliminate x
0.2x + 0.2y = 0.2(100)
0.2x + 0.2y = 20 ...equation (3)
Subtract equation 3 from 1
0.2x -0.2x + 0.3y - 0.2y = 25-20
0.1y = 5
y = 5/0.1 = 50
The amount of gallons of 30% of moonshine required = 50gallons
Substitute for y = 50 in equation 1
0.2x + 0.3(50) = 25
0.2x + 15 = 25
0.2x = 25-15
0.2x = 10
x = 10/0.2 = 100/2
x = 50
The amount of gallons of 20% of moonshine required = 50gallons
Therefore the 50 gallons of 20% of moonshine and 50 gallons of 30% of moonshine is required to make 100gallons of 25% moonshine mixture
