Question

To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions.

****Write the solution as an ordered pair.
I know it looks like the same question as the previous one I posted, but this one is different than the other one from the bottom. To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions.

****Write the solution as an ordered pair.
I know it looks like the same question as the previous one I posted, but this one is different than the other one from the bottom. @Mathematics

Answer 1

we can write the amount a person must pay as a function in terms of the flat rate+session fee*number of sessions (n)
\[f(n)=m+f*n\]

Answer 2

when he had attended n=5 sessions we have
25=m+5f
and when he had attended n=10 sessions we have
40=m+10f

subtract the second equation from the first and we get
15=5f
3=f
substituting that in to either equation we get
25=m+5(3)
10=m
or
40=m+10(3)
10=m

so our solution is m=10, f=3, or (m,f)=(10,3)

Answer 3

Perhaps I'm missing something, but why do you add the membership fee to the second session?

Answer 4

he paid 40 dollars in all, meaning membership + session fees

Answer 5

In all here meaning something akin to a cumulative payment?

Answer 6

If that's the case, wouldn't then 'm' be better replaced by 25? I don't know, I'm a little confused.

Answer 7

in all meaning m+nf meaning all payments towards it. it is the equivalent of saying a different person had been there 10 times and payed 40 dollars, but m shouldn't be 25 because the membership fee is not constant b/c otherwise he would have payed 25 dollars at both times