Posted by **Alicia** on Friday, November 16, 2007 at 10:55pm.

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:

Show your work here:

so for part 1 would be C = 35 + 4

- College Algebra -
**Reiny**, Friday, November 16, 2007 at 11:17pm
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, C_{1} = 35 + 4x

since he pays no monthly fee for option 2, wouldn't that equation be

C_{2} = 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

- College Algebra -
**Alicia**, Friday, November 16, 2007 at 11:21pm
I came up with 14 < x

- College Algebra -
**Reiny**, Saturday, November 17, 2007 at 12:41am
Ummmh?

Suppose I said 10 < 20

Could I say 20 > 10 ????

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