Answer to Question #168469 in Algebra for Elle

Question

Solve the problem.

A cellular phone plan had the following schedule of charges:

Basic service, including 100 minutes of calls$20.00 per month2nd 100 minutes of calls$0.075 per minute additional minutes of calls$0.10 per minute

What is the charge for 200 minutes of calls in one month?

What is the charge for 250 minutes of calls in one month?

Construct a function that relates the monthly charge C for x minutes of calls.

Answer 1

Basic service charge for per month for first 100 minutes is = $20

service charge for next 100 minutes is = $0.075 per minute * 100 minutes = $7.50

service charge for additional minutes is = $0.10 per minute

1).

the charge for 200 minutes of calls in one month is = 20 + 0.075*100 = $27.50

2).

the charge for 250 minutes of calls in one month is = 20+ 0.075*100+0.10*50 = $32.50

3).

A function that relates the monthly charge C for x minutes of calls is:

a).

C(x) = fixed cost for 100 min + cost for the next 100 min + (x-200) times 0.1 per minute

C(x) = 20 + 0.075*100 + 0.1(x-200)

(valid for x greater than or equal to 200)

b)

if value of x is less than or equal to 200 minutes and more than or equal to 100 minutes

C(x) = 20 + 0.075*(x-100)