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

50 gallons of each

Explanation:

When the mix percentage is halfway between the percentages of the constituents, they are mixed half and half.

50 gallons of 20% and 50 gallons of 30% have to be mixed to make 100 gallons of 25% moonshine.

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For the variable definitions in the problem statement, you can write the equations ...

x + y = 100

0.20x +0.30y = 0.25(100)

I like to use a single variable representing the greatest contributor. Along that line, we have ...

x = 100 -y

0.20(100 -y) +0.30y = 25 . . . . . substitute for x

20 +0.10y = 25 . . . . . . simplify

0.10y = 5 . . . . . . . . . . . subtract 20

y = 50 . . . . . . . . . . . . . multiply by 10

x = 100 -50 = 50

The mixture will be 50 gallons of each constituent.