equation needed

Question

A computer training institute has 625 students that are paying a course fee of $400. Their research shows that for every $20 reduction in the fee, they will attract another 50 students. Which equation could be used to represent this situation, where x is the course fee and R(x) is the total revenue?

Answer 1

First, derives the equation of the demand line... Q(x) where x is the price and Q is the enrollment;

the slope is +50/-20 = -5/2; When the price goes up the demand decreases and vice versa

(400,625) is on this line, per the given...

B = y - mx = 625 - (-5/2)(400) = 625 + 1000 = 1625

Q(x) = (-5/2)x + 1625

The revenue is R(x) = x(Q(x)) = x [ (-5/2)x + 1625 ]