Question

An internet company charges a one-time setup fee of $44.99 and a monthly fee of $29.99 for Internet service. The company is offering a 25% discount on the monthly fee for the first year.
Part A:Write an expression to determine the cost, after the discount and before tax, of m months of service during the first year. (remember that an expression is just like an inequality except there is equal sign than a less than or greater than sign and plz show work)

Part B:An 8% sales tax is added to the total cost. Rewrite the expression in Part A to include the sales tax.

Part C:What is the total amount a customer will pay, to the nearest cent, including tax, for the first 4 months of Internet service with the Internet company? (try to explain a little for these questions if u can)

Answer 1

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.