Question 150245
constant=cost in thousands *(so you have less zeros and it looks less confusing)
y=number of people
x=price per person


200/y=x
(200/y+5)=x-2


Substitute x
(200/y+5)=(200/y)-2


Common denominator on the right side=y
200/y+5=200/y - 2y/y


Combine like terms on the right side
200/y+5=200-2y/y


Cross multiply
200y=(y+5)(-2y+200)


FOIL the right side
200y=-2y^2+190y+1000


Subtract 200y from both sides
0=-2y^2-10y+1000


Factor out a negative 2
0=-2(y^2+5y-500)


Factor
0=-2(y+25)(y-20)


Solve for y
y+25=0
y=-25


y-20=0
y=20


You got two solutions, but since y=number of people, and the amount of people cannot be negative, you know that y=20 is your answer.


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