Question

Solve the following problem using substitution or elimination: To skate at Roller Heaven, each person must pay a monthly membership fee (m) and a fee for each session (f). In January, Art attended 5 sessions and paid $25 in all. In July, he attended 10 sessions, and he paid $40 in all. How much is the membership fee and how much are the session? Be sure to show all work.

Answer 1

1
The monthly membership fee is a constant, therefore, no matter how many sessions Art goes to, that fee will stay the same we will denote this as (x)

The fee for each session is a fee that is multiplied by the number of sessions he goes to, this will be denoted as (y)

First equation:
He did 5 sessions, therefore he paid the session fee five times, and the membership fee only once (Because it is a constant) so the equation is:

5y+x=25

Second Equation:
Using the same logic as before, we get the second equation for the month of July:

10y+x=40

Now we will substitute. Solve the first equation for x in terms of y to get x=25-5y and plug this into the second equation
10y+25-5y=40
Now that we have the equation in terms of one variable, solve for y:

5y=15
y=3
The session fee is $3

Plug y into the first equation to get: 30+x=40
and you get x=10
the membership fee is $10

Answer 2

Thanks Zhang

Answer 3

Monthly fee + 5f = $25
Monthly fee + 10f = $40

(Monthly fee - Monthly fee) + (10f - 5f) = ($40 - $25)

5f = $15
f/5 = $15/5

Divide 15/5.

Monthly fee + 5($3 sessions) = $25

Monthly fee + $15 = $25 - $15 - $15

Monthly fee = $10 and $3 per session.