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16 March, 22:49

16. Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.

a. If both of them get $4.50 an hour, write an inequality to compare Peter's and Cindy's earnings.

b. What should Cindy's per-hour income be so that she earns at least $14 a day? Write an inequality and an explanation of how to solve it.

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  1. 16 March, 23:13
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    Part A)

    4.50 * 3 > 4.50 * 2 13.5 0 > 9

    Part B)

    r ≥ 7

    Explanation:

    1) The earnings are calculated multiplying the number of hours by the hourly rate.

    2) The hourly rate of both Peter and Cindy is the same: $ 4.50 / hour

    3) Let the variable used for computing the number of hours be h.

    4) The number of hours Peter works every day is 3 hours, so, using the letter P to name Peter's earnings, the expression to calculate his earnings is:

    P = 4.50 * 3

    5) Similarly, the expression to calculate Cindy's earnings would be:

    C = 4.50 * 2

    Answering part A)

    You have to write an inequality to compare Peter's and Cindy's earnings:

    4.50 * 3 > 4.50 * 2 13.5 0 > 9

    This is, the earnings of Peter are greater than the earnings of Cindy.

    Part B),

    You have to write an inequality to calculate Cindy's per-hour income so that she earns at least $ 14 a day.

    Here, C ≥ 14, because the sign ≥ means greater than or equal to, meaning the the earnings are greater than or equal to 14.

    Thus, since she works 2 hours per day, the inequality becomes 2 * r ≥ $ 14, where r is the per-hour income.

    To solve it follow these steps:

    Given: 2r ≥ 14

    Divide both sides by 2: r ≥ 14 / 2

    Simplify: r ≥ 7

    That means that Cindy's per-hour income should be at least $7 and hour so that she earns $14 a day.
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