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algebra

posted by on .

could you please show me how to do this problem?
ballfield costs 14,850,00 to build. the cost per city resident to build it will be based on last census. New census shows population increased by 2200 people, which reduced the cost per resident $75. what is the current population of the city?? thank you

  • algebra - ,

    The way you grouped the cost by thousands, I think you left out a zero
    is it 14 850 000 ?

    let currect population be x
    last year's population is x - 2200

    currect cost per person = 14850000/x
    last year's cost per person = 14850000/(x-2200)

    14850000/(x-2200) - 14850000/x = 75
    14850000x - 14850000(x-2) = 75x(x-2200)

    75x^2 - 165000x - 14850000(2200) = 0
    x^2 - 2200x = 435 600 000
    x^2 - 2200x + 1210000 = 435 600 000 + 1 210 000
    (x - 1100)^2 = 436 810 000
    x - 1100 = 20900
    x = 22 000

    check:
    current pop: = 22000
    cost per person = 14850000/22000 = 675

    last years' pop = 19800
    cost per person = 14850000/19800 = 750

    change = 750-675 = 75 , YEAHH!

  • algebra - ,

    yes you were right about the zero. Thank you so much for showing me how to do it. ann

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