I hope this helps, I wrote the new equation each time you get a new number and where it should be placed
Central angle = 360 / 24 = 15 degrees
ARc length = r * theta, where theta is the angle in radians and r = radius
= 15 * 15 * pi/180
= 3.93 feet to nearest hundredth.
Area of sector = area of circle / 24 = pi*15^2 / 24 = 29.45 ft^2
17.5$ for every 5 bottles refilled. $3.50 for every 1 bottle refilled
= 2025
When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)
For this, you divide the given lengths using the numbers that divides all through.
I have added an image to this answer. Go through it for more explanation