Question:
The cost C (in dollars) for the care and maintenance of a horse and carriage is C = 15x + 2000 where x is the number of rides.
Rides cost 35$
A: write an equation for the revenue R in terms of the number of rides
B: How many rides are needed to break even
Answer:
The equation for revenue R in terms of number of rides is R(x) = 35x
100 rides are needed to break even
Solution:
Given is the cost function,
C(x) = 15x + 2000
where x is the number of rides
And rides cost 35$
Therefore, for "x" rides, revenue is given as:
R(x) = 35x
Thus the equation for revenue R in terms of number of rides is found
b. How many rides are needed to break even?
Break even point occurs, when at a certain point x the total cost equals to the total revenue.
At break even, cost = Revenue
C(x) = R(x)
15x + 2000 = 35x
35x - 15x = 2000
20x = 2000
x = 100
Therefore, 100 rides are needed to break even