need help i'm sooo lost with math?

Question

A tennis club offers 2 payment options:

option 1:
$35 monthly fee plus $4/hr for court rental.
option 2 : no monthly fee but $6.50/hr for court rental. let x = hrs per month of court rental time.

A) write a mathmatical model representing the total monthly cost, C, in terms of x for the following?

option 1:_________
option 2:_________

B) how many hours would you have to rent the court so that monthly cost of option 1, is less than option 2. set up an inequality & show your work algebraically using the info in part A.

Answer 1

A) 35+4x=c: because you have 35$ monthly fee no matter how much time you spend there you will always have a constant fee of thirty five dollars, then you add to it 4 times the amount of hours spent there because its 4$/hr which gives you 35+4x=c
6.5x=c: because the second option doesnt have a monthly fee you only have to worry about the hourly cost which is 6.50/hr so the second equation is 6.5x=C

B) Okey so you have two equations 35+4x=c(option 1) and 6.5x=C(option 2) and the question asks at what time (time = x) option 1 will be less than option 2
so: option1 < option 2
35+4x<6.5x
get the x's to one side by subtracting 4x from both sides
35<2.5x
get the x by itself so divide both sides by 2.5
14

Answer 2

Hi Jolene.

For option 1:

C = $35 + ($4)(x hours)

For option 2:

C = ($6.50)(x hours)

For part B, set up an equation of "equality" (then you can modify it to inequality).

Thus: For the price of option 1 to equal option 2:

$35 +($4)(x) = ($6.50)(x)

If we solve for x, we get $35 = 2.5x , thus
x = 14 hours

Thus, renting the court for 14 hours each month, the price of option 1 and option 2 is the same!

So, you have to rent the court MORE than 14 hours to make option one cost less than option 2.

Hope this helps you. Best wishes.

Answer 3

A)

Option 1: y=4x+35

Option 2: y=6.5x

B)

4x+35 < 6.5x

35 < 2.5x

14 < x

x > 14

You would have to rent the court for 15 hours.

Answer 4

A)
option1: C = 35 +4x
option2: C = 6.5x

B)
need to find when is (35+4x)>6.5
35>6.5x-4x
35>2.5x
therefore
x>14

this means option 1 is cheaper then option2 when the court is used for more then 14hrs, i.e 15hrs.

i think my maths is right but u better double check it makes sense to u.

Answer 5

1. 35+4t
2. 6.5t

35+4t=6.5t
2.5t=35
t=14

So price is equal at 14 hours, everything greater than that sees option 1 as the cheaper.

Answer 6

Option 1:
= $4.00x + $35.00

Option 2:
= $6.50x

B) No. of hours:
$4.00x + $35.00 > $6.50x
- $2.50x > - $35.00
x > 14

Answer: no. of hours per month must be less than 14 hours.