the phone company has two plans for cell phones. the first plan calls for a monthly fee of 35.00 with unlimited calling. The other plan is a monthly fee of 15.00, with a 0.50 fee for every minute over 100 used in a month. What is the greatest number of minutes that you can use in the second plan and still pay less than the first plan?

you want

15.00 + .5(m-100) < 35.00
m < 140

To determine the greatest number of minutes that you can use in the second plan and still pay less than the first plan, we need to compare the total cost of each plan.

Let's start by calculating the cost of the first plan, which has a fixed monthly fee of $35.00 with unlimited calling. Since there is no additional charge per minute, the total cost remains constant at $35.00, regardless of the number of minutes used.

For the second plan, we have a monthly fee of $15.00. In addition, there is a charge of $0.50 per minute for every minute over 100 used in a month.

To figure out the number of minutes at which the second plan becomes more expensive than the first plan, we need to determine when the cost of the second plan exceeds $35.00.

Let's set up the equation:
Cost of Second Plan > Cost of First Plan

We can express the cost of the second plan in terms of minutes:
Cost of Second Plan = $15.00 (monthly fee) + ($0.50 × M), where M is the number of minutes used over 100.

Now, we can arrange the equation:
$15.00 + ($0.50 × M) > $35.00

Next, let's isolate the variable M by subtracting $15.00 from both sides of the inequality:
($0.50 × M) > $35.00 - $15.00
($0.50 × M) > $20.00

Then, divide both sides of the inequality by $0.50 to solve for M:
M > $20.00 / $0.50
M > 40

The result of M > 40 means that the number of minutes used in the second plan must be greater than 40 minutes over 100 to exceed the cost of the first plan. Therefore, the greatest number of minutes that you can use in the second plan and still pay less than the first plan is 40 minutes over 100.