A dance studio charges $80 per student for a series of four 2-hour dance lessons. The studio's costs are $30

Question

per instructor. $15 per lesson for room rental & $3 per student misc. If x is the # of students enrolled , express the profit in terms of x. find the profit if 10 students enroll in the class.

Answer 1

Revenues are $80*X and if X=10, then $80*10 = $800.

You neglected to mention the teacher to student ratio!!!
I'll assume that there is 1 teacher per student.
Costs are $30*X + $15*4 + $3*X.
$80X - $30X - $60 - $3x = $47X - $60. $410 for x students.

If you assume 1 teacher per 10 students, then its:
Costs are $30 + $15*4 + $3*X.
$80X - $30 - $60 - $3x = $77X- $90. $680 for 10 students.

Answer 2

the best way to go about this is get everything into the same time frame, so lets say per session, so the cost per student is $20 per session for 4 sessions, the price of studio rental is $30, the instructor is $15 per sesion, student misc $3 per session per student, the cost to the student is $20, so

20s (s being # of students) - the cost of each student ($3s) = $17s - the cost of each lesson regardless of the students (-$30 for the studio and -$15 for the teacher) so
the equation PER SESSION is

$20s-$3s-$30-$15= $17s-$45, then multiply that equation by the # of sessions (4)so the equation then becomes

4($17s-$45) where s = 10 students, so 4($170-45) = 4($125)=$500

Answer 3

Let P be the profit
Let C be the total costs per student.
Let x = number of students

C= 4 * ($15/lesson rental) + ($30/instructor) + $3/ misc

P = x *($80 fee per student -C)

Combining we get
P = 80x- (30+18x) = 62x-30

When x = 10 that means a loss of $620-30 = $590 profit

That question is worded so loosely that it is not obvious which costs are per hour and which per student and how many teachers per class and whether the teachers are paid per student or per lesson. I think that is why you are getting answers that do not match.