math 1

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The total outing cost for a group of people amounted to Php 8000. When an additional 4 persons decided to join the outing, the cost per person decreased by 100. How many people actually joined the trip?

  • math 1 -

    let number of people originally be n
    cost per person = 8000/n

    new count = n+4
    new cost = 8000/(n+4)

    8000/n - (8000/(n+4) = 100
    times n(n+4)
    8000(n+4) - 8000n = 100n(n+4)
    expand after dividing by 100
    80n + 320 - 80n = n^2 + 4n
    n^2 + 4n - 320 = 0
    (n+20)(n-16) = 0
    n = 16 or n=-20 , but clearly n > 0

    so originally 16 people had signed up, but 4 more joined,
    So there were 20 people on the trip

    check:
    original cost = 8000/16 = 500
    new cost = 8000/20 = 400
    YUP!

  • math 1 -

    thanks Reiny, hope i am as intelligent as you.... :)

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