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31 January, 20:09

A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32. If a bus is charged $122, how many people do you think it contains?

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  1. 31 January, 20:34
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    38 people

    Step-by-step explanation:

    In this case, we can see that, being two people, the cost is 14 and when it is double, that is, 4 people, the value is not 28 but 20.

    Which means that there is an additional value that is being charged for the vehicle, that is:

    let "c" be the value of the vehicle and "x" be the value per person

    c + 2 * x = 14

    c + 4 * x = 20 = > c = 20 - 4 * x

    replacing:

    20 - 4 * x + 2 * x = 14

    -2 * x = 14-20

    -2 * x = - 6

    x = 6/2

    x = 3

    for C:

    c = 20 - 4 * 3

    c = 8

    Which means that the formula for the value of the input would then be:

    e = 8 + 3 * n

    where "n" is the number of people.

    Now, we are told that for e = 122

    122 = 8 * + 3 * n

    3 * n = 122 - 8

    n = 114/3

    n = 38

    which means that for that bus there are a total of 38 people
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