Question

Eastside Gym charges a $60 initial fee and $28.50 per month. Valley Gym charges $36 per month, and no initial fee. After how many months of use would Eastside cost less than Valley?
A. more than 8 months
B. more than 10 months
C. less than 7 months
D. more than 9 months

Answer 1

Do you know how to put this question into an equation?

Answer 2

noo

Answer 3

all right, so,

Eastside Gym charges a $60 initial fee and $28.50 per month.
This means that f(m) = 60 + 28.5m

Valley Gym charges $36 per month, and no initial fee
This means that f(m) = 0 + 36m

Do you understand?

Answer 4

(so far) ?

Answer 5

All I did was putting the question into some functions.

Eastside Gym charges a 60 initial fee and 28.5 per month.
This means that
total cost = 60 + 28.5*number of months.

In better notation:
f(m) = 60 + 28.5m.

Same thing for the other function.

Do you understand now?

Answer 6

so what will be my equation

Answer 7

Once you do, the next thing to realise is that we need to find the point at which the total cost for eastside gym is equal to the total cost of valley gym.

Putting this statement into a mathematical equation, you get:
60+28.5m = 0 + 36m

Now solve for m, and m will represent several things:

- the point at which the graph of the two lines intersect each other.
- the total amount of months, after which the total cost of east gym is equal to the total cost of valley gym.

So now you will have the point where they are equal. When will it be less then equal? at anything more than the intersect you just found. You can see this by graphing the two equation, I recommend you to do it if you find this confusing.

Answer 8

graphing the two functions*

Answer 9

ok hold on let me solve for m

Answer 10

will it be 8months

Answer 11

it will be 60/(36-28.5)

Answer 12

I think that is 8

Answer 13

this is my answer choice


A. more than 8 months
B. more than 10 months
C. less than 7 months
D. more than 9 months

Answer 14

Well I am not going to give you the answer. I hope I taught you how to solve these kind of problems though. Can you try find the answer yourself with the explanation I gave you?

Answer 15

i said its going to be 8 more than 8 months am i right or wrong

Answer 16

why do you think it is "8 more" than 8 months?

Answer 17

because i divide 60=7.5

Answer 18

60/7.5 = ?

Answer 19

ok then its less than 8

Answer 20

No. 60/7.5 = 8

Answer 21

But it is not 8 more than 8 months

Answer 22

Because at 8 months, we know that the total cost of EG = total cost of VG

Answer 23

so in fact, anything, even the smallest value, bigger than 8 months, EG will cost less than VG

Answer 24

so it will be less than then 7

Answer 25

why?

Answer 26

im confused than its has to be more then 9

Answer 27

You realise that EG will cost less than VG at 8 months right? That is what we just solved for!

Answer 28

thats why i said my answer will be more than 8

Answer 29

months

Answer 30

that is correct. But not "8 more than 8". Anything more than 8

Answer 31

thanks

Answer 32

No problem! :) Hope you understand how to solve these problems now! Good luck :)