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
