Question

You have recently begun reasearching phone billing plans. Phone company A charges a flat rate of $75 a month. A flat rate means that your bill will be $75 each month with no additional costs. The billing plan for Phone Company B is a linear function of the number of texts that you send that month. That is, the total cost of the bill changes each month depending on how many texts you send.

Answer 1

Complete question :

You have recently begun reasearching phone billing plans. Phone company A charges a flat rate of $75 a month. A flat rate means that your bill will be $75 each month with no additional costs. The billing plan for Phone Company B is a linear function of the number of texts that you send that month. That is, the total cost of the bill changes each month depending on how many texts you send.

Input (no of text) __ cost of bill

50 ______________ $50

150 ______________$60

200 _____________ $65

500 _____________ $95

At what number of text will be phone plan be the same ; At what Number of text is company A the better choice ; At what number of text is company B the better choice.

Answer:

Cost is the same at, x = 300

at number of text, x < 300 phone plan B is better ;

at number of text, x > 300 phone plan A is better

Step-by-step explanation:

Let cost = y

Let x = Number of text

Company A :

y = 75

company B :

y = mx + c

m = slope = (y2 - y1) / (x2 - x1) = (95 - 50) / (500 - 50) = 45 / 450 = 1/10

When y = 50, x = 50

50 = 1/10(50) + c

50 = 5 + c

c = 50 - 5 = 45

Company B:

y = 1/10x + 45

When charge will be the same :

75 = 1/10x + 45

75 - 45 = 1/10x

30 = 1/10x

300 = x

Cost of phoe plan is the same at number of text = 300

At text = 299

Company B :

y = 1/10(299) + 45

y = 74.9

Hence, at number of text, x < 300 phone plan B is better

At text = 301

Company B :

y = 1/10(301) + 45

y = 75.1

Hence, at number of text, x > 300 phone plan A is better