When selling lemonade for 50 cents per cup, Diana can sell 40 cups per day. She observes that the number of cups sold per day decreases by 2 for every 5-cent increase in the price of a cup of lemonade.

Question

Determine a formula for the number cups C of lemonade sold each day as a function of the price p in cents of a cup of lemonade if all price increases occur only in multiples of 5-cent increments.

Answer 1

c = cups/day
p = pennies/cup

dc/dp = -2/5

so
c = -(2/5) p + constant
when p = 50, c = 40
so
40 = -2*50/5 + constant
constant = 60
and
c = -(2/5) p + 60
now you can make that p = 5n if you choose where n is an integer
number of nickels
c = -2 n + 60