How Many Students Were Initially Planned for the History Class Trip?

[thua]

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.

 

[professor]

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)

 

[HallsofIvy]

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.

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.

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.

Start with (2+ 189/x)(x-6)= 189 and try again.

 

[thua]

i think i got it now... thanks a bunch!

 

[aspen308]

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]
or
(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