SOLUTION: There is an initiation fee to join the Wellness Center, as well as monthly dues. The total cost after 7 months' membership will be $335, and after 1 1/2 year, $830. Find both the i

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: There is an initiation fee to join the Wellness Center, as well as monthly dues. The total cost after 7 months' membership will be $335, and after 1 1/2 year, $830. Find both the i      Log On


   

Question 1010453: There is an initiation fee to join the Wellness Center, as well as monthly dues. The total cost after 7 months' membership will be $335, and after 1 1/2 year, $830. Find both the initiation fee and the monthly dues. Setup a system of equations and solve. Label your answers. Show step by step.
Thanks in advance!
Found 3 solutions by Cromlix, josmiceli, stanbon:
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
The total cost after 7 months' membership will be $335
Make initiation fee = x
Make monthly due = y
x + 7y = $335
and after 1 1/2 year, $830.
x + 18y = $830
..............
x + 7y = $335.......(1)
x + 18y = $830......(2)
Subtract (1) from(2)
....11y = $495
....y = $45
Substitute y = $45 in (1)
x + 7y = $335
x + 7($45) = $335
x + $315 = $335
x = $335 - $315
x = $20
Initiation fee = $20
Monthly due = $45
Hope this helps :-)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is a straight line relation and the slope is
[ dues ] / [ month ]
Let +C+ = total cost including initiation plus dues
Let +n+ = number of months the dues are paid
-----------------------------------------
Plot +C+ on the vertical axis and
plot +n+ on the horizontal axis
------------------------------
You are given the points:
( 7, 335 )
( 18, 830 )
Use the general point-slope formula
+%28+C+-+335+%29+%2F+%28+n+-+7+%29+=+%28+830+-+335+%29+%2F+%28+18+-+7+%29+
+%28+C+-+335+%29+%2F+%28+n+-+7+%29+=+495+%2F+11+
+11%2A%28+C+-+335+%29+=+495%2A%28+n+-+7+%29+
+11C+-+3685+=+495n+-+3465+
+11C+=+495n+%2B+220+
+C+=+45n+%2B+20+
-----------------
check answer:
( 7, 335 )
+C+=+45n+%2B+20+
+335+=+45%2A7+%2B+20+
+335+=+315+%2B+20+
+335+=+335+
and
( 18, 830 )
+C+=+45n+%2B+20+
+830+=+45%2A18+%2B+20+
+830+=+810+%2B+20+
+830+=+830+
OK
--------------------
The monthly dues is the slope of the line, so
dues = $45
The initiation fee is the intercept on the vertical
axis, found by setting +n+=+0+
+C+=+45%2A0+%2B+20+
+C+=+20+, so
initiation = $20
---------------
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+20%2C+-100%2C+1000%2C+45x+%2B+20+%29+
Here's a close-up of the C-intercept:
+graph%28+400%2C+400%2C+-1%2C+2%2C+-3%2C+30%2C+45x+%2B+20+%29+

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There is an initiation fee to join the Wellness Center, as well as monthly dues. The total cost after 7 months' membership will be $335, and after 1 1/2 year, $830. Find both the initiation fee and the monthly dues. Setup a system of equations and solve. Label your answers. Show step by step.
Equations:
f + (7/12)d = 335
f + (3/2)d = 830
-----
Subtract and solve for "d":
[(3/2)-(7/12)]d = 495
-----
[(36-14)/24]d = 495
(11/12)d = 495
(1/12)d = 45
---
dues = 12*45 = $540
----
Solve for "f":
f + (3/2)d = 830
f = 830-(3/2)540
fee = 830-818 = $12
-----
Cheers,
Stan H.
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