PART A :
let cost, after the discount and before tax, of m months = x
The cost will have two parts
1) a one-time setup fee of $44.99
2) monthly fee for m months including discount
monthly fee = $29.99
for m months , fee = 29.99 × m = 29.99m
from the given statement "m months of service during the first year" we can say that discount of 25% will be applicable for m months.
for m months , fee after pplying discount = 29.99m - 25% of 29.99m
= 22.4925m
so total cost = a one-time setup fee + monthly fee for m months including discount
hence required expression is as follows
⇒ x = 44.99 + 22.4925m ------------ expression 1
where x is cost in $ and m is number of months kess than or equal to 12
PART B :
let total cost including sales tax = y
so y = x + 8% of x [ where x is cost calculated in part A ]
⇒ y = x + 8x/100
⇒ y = 108x/100 = 1.08x
⇒ y = 1.08 ( 44.99 + 22.4925m ) [ substituting value of x from expression 1 ]
⇒y = 48.5892 + 24.2919m
so cost after including sales tax will be given by following expression
y = 48.5892 + 24.2919m ------------ expression 2
where y is cost in $ and m in number of months less than or equal to 12.
Part C :
As total cost including sales tax is represented by expression 2 that is
y = 48.5892 + 24.2919m
when m = 4 months
y = 48.5892 + (24.2919 × 4)
y = 48.5892 + 97.1676
= 145.7568.
so the total amount a customer will pay including tax, for the first 4 months of Internet service will be $ 145 and 76 cents.
the above all equations will only hold true for first years , after that discount will not be in place.
