Question

Moonshine Problem: How many gallons of 20% moonshine and how many gallons
of 30% moonshine have to be mixed together to make 100 gallons of 25%
moonshine?
(x
= gallons of 20% moonshine; y = gallons of 30% moonshine.
20% moonshine is called 20% because 20% of any amount (like x) is PURE
MOONSHINE!)​

Answer 1

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