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1 March, 13:54

A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to the one-way fare, 100 passengers will find other means of transportation. Let x represent the number of $1.00 increases in ticket price. Choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000. Then, use the inequality to select all the correct statements.

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  1. 1 March, 13:57
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    I can determine the inequality with the information provided. Then, from that you may select the correct statements given that you did not include them.

    Determination of the inequality:

    1) Revenue = number of riders * price of the ticket ≥ 12

    2) number of riders = 2000 - 100x [x is the number of $1.00 increases on the price]

    3) price = 5 - x

    4) Equation, revenue = (2000 - 100x) (5 - x) = 10,000 - 2,000x - 500x + 100x^2

    revenue = 10,000 - 2500x + 100x^2

    5) Inequality 10,000 - 2500x + 100x^2 ≥ 12,000

    6) Simplify the inequality:

    10,000 - 12,000 - 2500x + 100x^2 ≥ 0

    - 2,000 - 2500x + 100x^2 ≥ 0

    -20 - 25x + x^2 ≥ 0

    There you have to forms of the inequality. Sure, other equivalent forms can be displayed.

    Analysis and conclusion:

    From that you can determine that it is not possible to reach the revenue of 12,000 under the conditions given.

    Note that the domain of x is 1, 2, 3, 4, 5.

    When you solve the inequality, you realize that none value of x between 0 and 5 result in a revenue greater than or equal to 0.

    So, the conclusion is that it is not possible to have a revenue of at least 12,000.
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