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?

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?

hero · Answer

(5,25) and (10,40) plot and find the slope. Then use the point slope formula

anonymous · Answer

25=m+5f
40=m+10f
-25=-m-5f
15=5f
f=3
m=10

anonymous · Answer

m + 5f = 25
m + 10f = 40
m = 25 - 5f
(25 - 5f) + 10f = 40
etc

hero · Answer

or you can do that

anonymous · Answer

It does say using substitution etc ;)

hero · Answer

I know. I was just showing another way it could be solved.

anonymous · Answer

(25 - 5f) + 10f = 40 
So then I solve this by subracting 5f from both sides right?

myname · Answer

let x be the total monthly fee
let y be the cost per session
Then we can get
x+5y=25
x=25-5y
Again,
x+10y=40
 Now, we can substitute the value of x and solve for y 
25-5y+10y=40
5y=40-25
y=15/5=3
Now , we can find x by using one of the above eq
x=25-5(3)
x=10
Thus the total monthly fee is 10$ and the fees per session is 3$