Question

A tennis club offers two payment options:
Option1: $35 monthly fee plus $4/hour for court rental
Option 2: No monthly fee but $6.50/hour for court rental.
Let x = hours per month of court rental time.
a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:
Option 1: C= _________________
Option 2: C=_________________
b) How many hours would you have to rent the court so that the monthly cost of option 1, is less than option 2. Set up an inequality and show your work algebraically using the information in part a.

Answer 1

Multiply the cost per hour by number of hours x and for option 1 you need to add the monthly fee:

A) option 1: C= 4x +35

Option2: C = 6.50x

B)

4x+35 < 6.50x

Subtract 4x from both sides:

35 < 2.50x

Divide both sides by 2.50 :

X < 14

You would need to rent more than 14 hours for option 1 to be cheaper.