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

Question

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.

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Bella 2 weeks 2022-01-07T00:40:39+00:00 1 Answer 0 views 0

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    2022-01-07T00:42:16+00:00

    Answer:

    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

    3x+100

    Cost Plan B

    5x

    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

    3x+100 < 5x

    solve for x

    subtract 3x both sides

    100< 5x-3x\\100<2x

    divide by 2 both sides

    50 < x

    Rewrite

    x> 50\ min

    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

    3x+100

    Cost Plan B

    5x

    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

    3x+100= 5x

    solve for x

    5x-3x=100\\2x=100\\x=50\ min

    therefore

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

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