a) The actual yearly cost of the membership is $46
b) $2900 amount of club purchases will reduce the actual yearly cost of the membership to $42.
c) a member have to spend $5000 yearly in club purchases to reduce the yearly membership cost to $0.
We have been given the linear equation which is
y = 100 – 0.02x (1)
where, y = actual yearly cost of the membership in dollars.
x = yearly amount of club purchases in dollars.
a ) we have to find the actual yearly cost of the membership if the club purchases for the year is $2700.
Here we have been given the value of x which $2700. Thus we have to find the value of y from the given model. Putting the value of x in equation (1) we get
y = 100 – 0.02*2700
y = 100-54
y = 46
therefore, the actual yearly cost of the membership is $46
b) We have to find the amount of club purchases that would reduce the actual yearly cost of the membership to $42.
Here we have been given the value of y which is $42. Thus we have to find the value of x from the given model. Putting the value of y in equation (1) we get
42 = 100 – 0.02x
-58 = -0.02x
x = 2900
therefore, $2900 amount of club purchases will reduce the actual yearly cost of the membership to $42.
c) According to the statement, we have been given the value of y which is $0. Thus we have to find the value of x from the given model. Putting the value of y in equation (1) we get
0 = 100 – 0.02x
-100 = -0.02x
x = 5000
therefore, a member have to spend $5000 yearly in club purchases to reduce the yearly membership cost to $0.
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