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Quadratic Equation Problem

  1. Oct 24, 2005 #1
    Students from a history class prepare a trip that will cost them a total of $189 that will be shared between them. The day before the trip, 6 students discovered that they can't participate in the trip. To avoid cancellation, the rest of the class decided to pay an additional $2 each.
    How many students are there in this class?

    I have:
    (x-6) = the number of students going
    189/x = the cost for the whole class before the 6 students couldn't go

    2(x-6) + 189/x = 189 <=== not sure if this is even right.
    2x - 12 + 189/x = 189
    2x^2 - 12x + 189 = 189x
    2x^2 - 201x + 189
    2(x^2 - 100.5x) + 189
    2(x - 50.25)^2 - 5050.125 + 189
    2(x - 50.25)^2 - 4861.125

    That doesn't seem to make sense. So I hope you can help me.
  2. jcsd
  3. Oct 24, 2005 #2
    this first needs to be set to a quadradic equation as your title suggests, there should be an x and a y this is because the number of students correlates with the amount each student has to pay (or the amount they would have had to pay before the 6 students left)
  4. Oct 24, 2005 #3


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    You have every right to be unsure! Think about what each part means. x- 6 is the number of students who are going and I assume the "2" is the $2 extra each is paying so 2(x- 6) is the total extra money paid. But "189/x" is the amount each was paying before. Surely you don't want to add the total extra and the amount each was paying. I think what you intended to say was that, previously each was paying 189/x and now each of those who is going must pay an additional $2- so the amount each of the persons going pays is 2+ 189/x. Now that is the amount paid by x- 6 people: (2+ 189/x)(x-6)= 189.

    Start with (2+ 189/x)(x-6)= 189 and try again.
  5. Oct 24, 2005 #4
    i think i got it now... thanks a bunch!!
    Last edited: Oct 24, 2005
  6. Sep 7, 2008 #5
    let x = Initial number of students in the group
    189/x = cost per student

    when 6 students discovered they cannot participate
    x-6 = resulting number of students after the 6 was unable to go with the group
    this leads to 189/x-6 being the cost divided among remaining students

    To avoid cancellation [(189/x) +2] =amount the rest of the class decided to pay.

    In order for the trip to push through:

    (189/x-6) = [(189/x) +2]
    (189/x-6) - 189/x = 2

    x^2 -6x-567 = 0

    x= [6+/- (sqrt (36+4*567))]/2=27 (discarding the negative root)

    therefore x=27 is the original number of students
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