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28 March, 07:41

A rappelling club charters a bus for a trip to the mountains for $540. To lower the bus fare per person, the club invites some hikers on the trip. After 7 hikers join the trip, the bus fare per person decreases by $7. How many members of the rappelling club are going on the trip?

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  1. 28 March, 09:10
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    20 members of the rappelling club are going on the trip

    Explanation:

    Total cost of the trip is $540.

    If only one person goes, the cost is $540.

    We can make the total number of people going x since we are not given.

    Therefore, each member would pay (540/x)

    We can also rep 7 with non members since the number is given as 7

    Total people going = Members + non members.

    Therefore, the cost per person is now (540/x+7).

    Problem.

    540/x - 540/x + 7 = 7

    Multiply each with lowest common denominator.

    When you expand, you get

    540 (x+7) - x (540) / x (x+7) = 7

    Simplify multiplication.

    540x+3780-540x=7 (x^2+7x)

    Combine like terms

    540x-540x+3780=7x^2+49x

    3780=7x^2+49x

    7x^2+49x-3780 = 0

    When we divide through by 7, we have

    x^2+7x-540

    Factorize, we have

    (x^2+27x) - (20x-540) = 0

    x (x+27) - 20 (x+27) = 0

    (x-20) (x+27) = 0

    x is therefore 20 or - 27

    Since we know - 27 cannot be a reasonable answer hence must be excluded.

    The exact number of the people going on the trip is 20.
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