SOLUTION: A tennis club offers two payment options: Option1: $32 monthly fee plus $3/hour for court rental Option 2: No monthly fee but $6.50/hour for court rental. Let x = hours per m

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Question 188866: A tennis club offers two payment options:
Option1: $32 monthly fee plus $3/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. Round to 3 decimal places if necessary.
Answer by jonvaliente(64) About Me  (Show Source):
You can put this solution on YOUR website!
a) Option 1: C=32%2B3%2Ax
Option 2: C=6.5%2Ax
b) %2832%2B3%2Ax%29%3C%286.5%2Ax%29

Subtract 3*x from both sides
32%3C3.5%2Ax

Divide both sides by 3.5
9.143%3Cx
This means that you have to rent the court for more than 9.143 hours so that Option 1 payment option is less than Option 2