ethan goes on vacation with $1100 for his expenses. if he extends his vacation by 2 days, he has to cut down his daily expenses by $5.find the original duration of his vacation
free points

20 days
x=number of days vacation
y=daily expenses
xy=1100
(x+2)(y-5)=1100

xy-5x+2y-10=1100
xy-5x+2y=1110
y=1100/x
x(1100/x)-5x+2(1100/x)=1110
1100-5x+(2200/x)=1110
-5x+(2200/x)=10
-5x^2 + 2200 = 10x
-x^2 + (440) = 2x
x^2 - 440 + 2x = 0
(x+22)(x-20)=0
x=-22,20
only take the positive answer because the negative answer doesn't make sense in the question
so the answer is 20

I might be wrong; this question probation should've been this hard so I might have taken a wrong turn somewhere. feel free to double check my work

I’m not sure about that