What is the cost C (in dollars) for the care and maintenance of a horse and carriage is C+15x+200 where x is the number of rides.

Write an equation for the Revenue R in terms of the number of rides.

R=

How many rides are needed to break even?

You didn't specify how much is charged per ride to determine revenue ... but we can just use a variable p for the price charged per ride ...

r (x) = px, c (x) = 15x+200

To break even, P, profit must equal zero and P (x) = r (x) - c (x)

P (x) = px-15x-200

P (x) = 0 when x (p-15) - 200=0

x=200 / (p-15)

So the number of rides needed, x, can be found once you determine what is charged per ride. : D * note from even this partial answer that p must be greater than 15 or you will never break even.