Answer:
The number of students who actually attended the prom are 200.
Step-by-step explanation:
Let the number of students attending the prom = x.
The total cost of the prom shared by the students attending is $17,850.
So, the cost for one person is [tex]\frac{17,850}{x}[/tex] dollars.
As, when 10 students could not attend the prom, the price per student increased by $4.25.
So, we get the equation,
[tex](x-10)(\frac{17,850}{x}+4.25)=17850[/tex]
i.e. [tex]17850-\frac{17,850}{x}+4.25x-42.5=17850[/tex]
i.e. [tex]-\frac{17,850}{x}+4.25x-42.5=0[/tex]
i.e. [tex]-17,850+4.25x^2-42.5x=0[/tex]
i.e. [tex]-42000+x^2-10x=0[/tex]
i.e. [tex]x^2-10x-42000=0[/tex]
i.e. [tex](x+200)(x-210)=0[/tex]
i.e. x= -200 and x= 210.
Since, x represents the number of students, which cannot be negative.
So, we have, x = 210
Thus, the number of students who actually attended the prom = x- 10 = 210 - 10 = 200
Hence, the number of students who actually attended the prom are 200.
