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)
Accepted Solution
A:
PART A :let cost, after the discount and before tax, of m months = xThe cost will have two parts1) a one-time setup fee of $44.992) monthly fee for m months including discountmonthly fee = $29.99for m months , fee = 29.99 × m = 29.99mfrom 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 = 22.4925mso total cost = a one-time setup fee + monthly fee for m months including discounthence required expression is as follows⇒ x = 44.99 + 22.4925m ------------ expression 1where x is cost in $ and m is number of months kess than or equal to 12PART B :let total cost including sales tax = yso 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 expressiony = 48.5892 + 24.2919m ------------ expression 2where 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 isy = 48.5892 + 24.2919mwhen m = 4 monthsy = 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.