Question

the total cost of prom this year was 17850. The cost was to be shared equally by those who planned to attend. Regrettably, at the last minute, 10 people could not attend, raising the cost for each person by $4.25. Determine the number of students who actually attended prom

Answer 1

The number of students who actually attended the prom are 200.

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
`(17,850)/(x)` dollars.

As, when 10 students could not attend the prom, the price per student increased by $4.25.

So, we get the equation,

`(x-10)((17,850)/(x)+4.25)=17850`

i.e.
`17850-(17,850)/(x)+4.25x-42.5=17850`

i.e.
`-(17,850)/(x)+4.25x-42.5=0`

i.e.
`-17,850+4.25x^2-42.5x=0`

i.e.
`-42000+x^2-10x=0`

i.e.
`x^2-10x-42000=0`

i.e.
`(x+200)(x-210)=0`

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.