math question 5?

Question

A tennis club offers two payment options:
Option 1: $42 monthly fee plus $5/hour for court rental
Option 2: No monthly fee but $8.50/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 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:
Show your work here:

Answer 1

Option 1: C=42+5x
Option 2: C=8,5*x

42+5x < 8,5*x
42< 8,5*x-5x
42<3,5x
42/3,5
420/35 < x

x>12

answer: 13 hours

Answer 2

Let x = no. of hours court rental.

$42 + $5x = $8x
$42 = $3x
x = 14

The court must be rented more than 14 hours a month for a monthly savings of $3 for every hour over and above 14 hours. Assume court rental of 15 hours (the savings will $3).

Cost:
Option 1:
$42 + ($5 * 15) = $42 +$75 = $117

Option 2:
$8 * 15 = $120

Option 2 is greater by $3 ($120 - $117) as compared to Option 1.