Question

The function f(x)=70n -400 models the profit of the instructor of a guitar class per month, where n is the number of students enrolled in the class. How many students must be enrolled in the class for the instructor to make a profit? How many students must be enrolled in the class if the instructor needs to make 1,000.00 profit per month?

Answer 1

Given:
f(x) = 70n - 400   : equation for monthly profit.
n = number of students enrolled in the guitar class.

70 refers to the amount charged per student.
400 is the fixed expense made by the instructor.

For the instructor to have a profit, the product of 70n must be more than 400.

400/70 = 5.7 or 6

There must be at least 6 students enrolled in class for the instructor to generate profit.

f(x) = 70(6) - 400 = 420 - 400 = 20

1000 = 70n - 400
1000 + 400 = 70n
1400 = 70n
1400/70 = n
20 = n

There must be 20 students enrolled in class for the instructor to earn 1000 in profit.

1000 = 70(20) - 400
1000 = 1400 - 400
1000 = 1000