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!)

50 gallons 20%

50 gallons 30%

Step-by-step explanation:

If x is gallons of 20% moonshine, and y is gallons of 30% moonshine, then:

x + y = 100

0.20x + 0.30y = 0.25(100)

Solve the system of equations using substitution or elimination.  Using substitution:

0.20x + 0.30(100 − x) = 0.25(100)

0.20x + 30 − 0.30x = 25

5 = 0.10x

x = 50

y = 50

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

the answer is a) y= 2 csc [0.5 (x+pi/2)]-1

step-by-step explanation: