A tennis club offers two payment options:

Question

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:
Show your work here:

so for part 1 would be C = 35 + 4

Answer 1

The amount he pays is a function of the number of hours he plays, you make no mention of that in your equation

for option 1, C₁ = 35 + 4x

since he pays no monthly fee for option 2, wouldn't that equation be
C₂ = 6.5x ???

b) just translate the English into math
"..monthly cost of option 1, is less than option 2."

35 + 4x < 6.5x

-2.5x < -35
x > 14

notice that for 14 hours the two costs would be the same , but for more than 14 hours option 1 would be cheaper

Answer 2

I came up with 14 < x

Answer 3

Ummmh?

Suppose I said 10 < 20
Could I say 20 > 10 ????