Question

Wo Internet service providers charge an installation fee plus a monthly service fee. The table shows the total costs in dollars) for different numbers of months at Company A. The total cost y (in dollars) for x months of service at Company B is represented by y=45x+50 . Which company charges less per month?
Company A
Months, x Total cost, y
2

3

4

5

6

$180

$220

$260

$300

$340


Company A
Company A

Company B
Company B
Question 2
After how many months of service are the total costs the same?
After___ months of service, the total costs are the same.

Answer 1

Using linear equations, we determined that:

1. Company A charges less per month

2. After 10 months of service, the total costs are the same.

How to Write Linear Equations?

We are given that:

• Number of months is represented as x
• Total cost is represented as y

Total cost for Company B is represented as y = 45x + 50.

Company B charges $45 per month.

Write an equation in slope-intercept form, y = mx + b, to represent the total cost y (in dollars) for x months of service at Company A. From the table given, using two pairs of values, (2, 180) and (3, 220), find the slope (m).

Slope (m) = change in y/change in x = (220 - 180)/(3 - 2)

Slope (m) = 40

Company A charges $40 per month.

Plug in m = 40 and (x, y) = (2, 180) into y = mx + b, to find the y-intercept, b:

180 = 40(2) + b

180 - 80 = b

b = 100

Substitute m = 40 and b = 100 into y = mx + b:

y = 40x + 100 (equation for Company A)

Make both equations equal to find the value of x, which is the number of months of service that will make the total costs of both company the same.

45x + 50 = 40x + 100

45x - 40x = -50 + 100

5x = 50

x = 10

Therefore, number of months would be 10.

In summary, using linear equations, we determined that:

1. Company A charges less per month

2. After 10 months of service, the total costs are the same.

Learn more about linear equation on:

brainly.com/question/2030026

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