Question

Dominic is comparing cellular plans. Company A charges a $175 start-up fee and $75 per month for service. Company B has no start-up fee but charges $97 per month. Which inequality will help Dominic figure out how many months it will take before the average monthly cost of Company A is less than Company B?

Answer 1

To determine the number of months it will take for Company A to have a lower average monthly cost than Company B, set up an inequality: 75x + 175 < 97x. Simplify and solve the inequality to find that it will take at least 8 months.

Step-by-step explanation:

To determine how many months it will take before the average monthly cost of Company A is less than Company B, we need to compare the monthly costs of both companies.

Let's assume the number of months required for Company A to have a lower average monthly cost than Company B is 'x'.

For Company A, the monthly cost can be represented as '75x + 175', and for Company B, the monthly cost is '97x'.

So the inequality to determine the number of months is: 75x + 175 < 97x.

Simplifying this inequality, we subtract '75x' from both sides to get '175 < 22x', and then divide both sides by '22', which gives 'x > 7.95'.

Therefore, it will take at least 8 months before the average monthly cost of Company A becomes less than Company B's.