Kendra is considering two different long-distance phone plans. Phone plan A charges a $100 sign-up fee and 3 cents per minute. Phone plan B does not charge a sign-up fee, but it charges 5 cents per minute.

Part 1) The number of minutes in a month must be greater than 50 in order for the plan A to be preferable

Part 2) The number of minutes in a month must be equal to 50 minutes

Step-by-step explanation:

The question is

Part 1) How many minutes would Kendra have to use in a month in order for the plan A to be preferable? Round your answer to the nearest minute

Part 2) Enter the number of minutes where Kendra will pay the same amount for each long distance phone plan

Part 1)

Let

x ---> the number of minutes

we have

Cost Plan A

Cost Plan B

we know that

In order for plan A to be cheaper than plan B, the following inequality must hold true.

cost of plan A < cost of plan B

substitute

solve for x

subtract 3x both sides

divide by 2 both sides

Rewrite

therefore

The number of minutes in a month must be greater than 50 in order for the plan A to be preferable

Part 2)

Let

x ---> the number of minutes

we have

Cost Plan A

Cost Plan B

we know that

In order for plan A cost the same than plan B, the following equation must hold true.

cost of plan A = cost of plan B

substitute

solve for x

therefore

The number of minutes in a month must be equal to 50 minutes

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3