Question

The function, f(x)=70n-400, models the profit the instructor of 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?

Answer 1

The instructor wants the profit to be positive, so
  f(n) > 0
  70n -400 > 0
  n - 400/70 > 0
  n > 5 5/7

The instructor must enroll at least 6 students to make a profit.

Answer 2

Answer:

6 students.

Step-by-step explanation:

We have been given a function $f(x)=70n-400$ that models  the profit the instructor of guitar class per month, where n is the number of students enrolled in the class.

We can see that 400 represents the amount of fixed expenses to run the guitar class by instructor and 70 represents the amount charged by instructor per student.

To make an profit the amount collected from n students minus the fixed charges must be greater than 0. So we can set up an inequality to solve for n as:

$70n-400>0$

$70n-400+400>0+400$

$70n>400$

Dividing both sides of our inequality by 7- we will get,

$\frac{70n}{70}>\frac{400}{70}$

$n>5.71428571$

Since 0.714 of a students can not be enrolled, so we will round up our answer.

$n>6$

Therefore, 6 students must be enrolled in the class for the instructor to make a profit.