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

To find the number of devices for which the cost of the new plan is less than the cost of the current plan, we need to set up an inequality.

Let's represent the number of devices as x.

The cost of the current plan is a flat rate of $175 per month.

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

So, the cost of the new plan is given by: 94 + 4.50x.

We want to find the number of devices, x, for which the cost of the new plan is less than the cost of the current plan, which is represented by the inequality:

94 + 4.50x < 175.

To solve this inequality, we can subtract 94 from both sides to isolate the variable:

4.50x < 175 - 94.

Simplifying the right side:

4.50x < 81.

Now, divide both sides by 4.50 to solve for x:

x < 81 / 4.50.

x < 18.

Therefore, for any number of devices less than 18, the cost of the new plan will be less than the cost of the current plan.