There is an initiation fee to join the River Country Club, as well as monthly dues. The total cost after 7 months' membership will be $3,125, and after 11/2 years, $3,950. Find both the initiation fee and the monthly dues.
initiation fee $
monthly dues $
Let X = initiation fee
X + 18m = 3950
X + 7m = 3125
Subtract second equation from first to solve for m. Insert value into either equation to solve for X.
To find the initiation fee and the monthly dues, we will set up a system of equations using the given information.
Let's assume the initiation fee is represented by "x" and the monthly dues are represented by "y".
From the information given, we can set up the following equations:
Equation 1: 7y + x = $3,125
Equation 2: (11/2)y + 18x = $3,950
Now we can solve this system of equations to find the values of x and y.
First, let's solve Equation 1 for x:
x = $3,125 - 7y
Next, substitute this expression for x in Equation 2:
(11/2)y + 18($3,125 - 7y) = $3,950
Simplify and solve for y:
(11/2)y + $56,250 - 126y = $3,950
(11y/2) - 126y = $3,950 - $56,250
(11y/2) - 126y = -$52,300
To simplify further, let's multiply the entire equation by 2 to get rid of the fraction:
11y - 252y = - $104,600
-241y = - $104,600
Divide both sides by -241 to isolate y:
y = (- $104,600) / (-241)
y ≈ $434.02
Now we can substitute this value of y back into Equation 1 to solve for x:
x = $3,125 - 7($434.02)
x = $3,125 - $3,038.14
x ≈ $86.86
Therefore, the initiation fee is approximately $86.86 and the monthly dues are approximately $434.02.