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 the number of devices, x, for which the cost of the new plan is less than the cost of the current plan.

Answer 1

Step-by-step explanation:

Here we know that 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. Assuming just a month, we can write a constant equation given by the form:

`y=175 \\ \\ \\ Where: \\ \\ y:\text{Cost in dollars}`

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

`y=94+4.5x \\ \\ \\ Where: \\ \\ x:\text{Number of months} \\ \\ y:\text{Number of devices}`

So we need to find the number of devices, x, for which the cost of the new plan is less than the cost of the current plan. By using inequalities:

`94+4.5x<175 \\ \\ 4.5x<81 \\ \\ x<(81)/(4.5) \\ \\ x<18`

So you should connect less than 18 devices in a month in order for the cost of the new plan to be less than the cost of the current plan.