SOLUTION: I tried this word problem then I got stuck. Thank you for helping! The cost of a gym membership includes the initial fee and a monthly fee. Find the initial and monthly fees if

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I tried this word problem then I got stuck. Thank you for helping! The cost of a gym membership includes the initial fee and a monthly fee. Find the initial and monthly fees if       Log On


   

Question 905686: I tried this word problem then I got stuck. Thank you for helping!
The cost of a gym membership includes the initial fee and a monthly fee. Find the initial and monthly fees if the total cost for five months is 225$, and the total cost for 10 months is 375$.
Let: I= initial M= Monthly
System:
5I+M=225
10I+M=375
5I+m=225
I=45-M
5I+8.33=225
I=43.33
10(45-M)+m=375
450-10M+M=375
M=8.3
Thanks!
Found 3 solutions by josmiceli, Math_Boss, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +I+%2B+5M+=+225+
(2) +I+%2B+10M+=+375+
----------------------
Subtract (1) from (2)
(2) +I+%2B+10M+=+375+
(1) +-I+-+5M+=+-225+
+5M+=+150+
+M+=+30+
and
(1) +I+%2B+5%2A30+=+225+
(1) +I+=+225+-+150+
(1) +I+=+75+
The initial fee is $75
The monthly fee is $30
-----------
check:
(2) +I+%2B+10M+=+375+
(2) +75+%2B+10%2A30+=+375+
(2) +375+=+375+
OK


Answer by Math_Boss(45) About Me  (Show Source):
You can put this solution on YOUR website!
Let: I= initial M= Monthly
System:
I+5M=225
I+10M=375
==========
I=225-5M
(225-5M)+10M=375
225+5M=375
5M=150
M=30
I=225-5x30=75
Ans:I=$75, M=$30


Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
I for initiation fee;
M for monthly fee.

5 MONTHS, I%2B5M=225.

10 MONTHS, I%2B10M=375.

Notice that the member pays the initiation fee only 1 time. He pays the monthly fee EACH MONTH.