Question

For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. Find the total number of visits when the cost for a member and nonmember will be the same

Answer 1

@rajathsbhat

Answer 2

ok let's model an equation which will tell us how much you'll be shelling out if you're
a) a member and
b) a non member.

Suppose you're a member. You first give $360 and $4 for every day (for the eqpt)
If you only go there for one day in that year, you'll be paying
360 + 4
If you go there for 2 days, you pay
360 + 4 + 4
For 5 days, you pay
360 + 4 + 4+ 4 + 4+ 4 = 360 + 4(5).

Now, if you go there for 'x' days in that year, you pay
360 + 4(x).

Do you get it?

Answer 3

yeah ido so ill do 360(4) then add it to 360

Answer 4

no no you can do that if you go there for the whole year. But you're not doing that.

Answer 5

the member will pay 360 for the "membership" PLUS 4 dollars for everyday. The non-member will pay $16 everyday.
So you want to see how many days it'll be until a member and non-member end up paying the same amount. You know what i mean?

Answer 6

ohhh i see

Answer 7

A.

480 days





B.

175 days





C.

60 days





D.

30 days

Answer 8

yeah :)
the non-member will pay only $16 if he goes there for only one day in that year.
He'll pay $32 for 2 days i.e. 16(2)
If he goes there for x days, he'll pay 16(x) okay?
so to find the no of days till they pay the same thing you equate the two models.
360+4(x)=16(x)

Finding x will mean finding the no of days...

Answer 9

Tell me what you get for x. I'm interested.

Answer 10

D 30 days
thanks

Answer 11

yw :)

Answer 12

ohh yeah i forgot wat is plottinglike in graphing

Answer 13

plotting is just putting points on a graph

Answer 14

ohh ok

Answer 15

:)