Question

An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.

Answer 1

`x<18`

Explanation:

Current plan : customers are charged a flat rate of $175 per month.

The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network.

Let the number of devices be x

Charge of 1 device = $4.50

Cost of x devices = $4.5x

So, total charge of new plan = 94+4.5x

Now we are given that the number of devices, x, for which the cost of the new plan is less than the current plan.

`94+4.5x<175`

`4.5x<175-94`

`4.5x<81`

`x<(81)/(4.5)`

`x<18`

Thus no. of devices cannot be more than of equal to 18 .

Refer the attached graph.

Answer 2

Cost of the current plan: $175
Number of devices: x
Cost of the new plan: $94+($4.50/device)x

Cost of the new plan is less than the current plan:
$94+($4.50/device)x<$175

Solving for x:
$94+($4.50/device)x-$94<$175-$94
($4.50/device)x<$81
(device/$4.50)($4.50/device)x<(device/$4.50)($81)
x<18 devices

Please, see the attached file.
Thanks.