Hello,Originally Posted byusm_67

Let be x = number of students (keep in mind that this x must be a natural number because 1.5 students are quite a funny sight)Originally Posted byusm_67

Let be p(x) = profit with respect to the number of students.

Then is the quadratic equation you're looking for.

If he sells 0 (zero) packages to 0 (zero) students his profit will be zero (0). So the c of the quadratic equation becomes zero (0):Originally Posted byusm_67

Now plug in the values you know. You'll get 2 linear equations:

0 = a*144+b*12

2000=a*256+b*16

Solve for a and b and you'll get: a = 31.25 and b = -375

Plug in 18 for x:Originally Posted byusm_67

Plug in 875 for p(x):Originally Posted byusm_67

This is a quadratic equation in x. Solve for x and you'll get:

x = 14 or x = -2.

(The (-2) students are the missing ones, which will appear in July when the snow has melted away)

Greetings

EB