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

At least 6 students must be enrolled in the class for the instructor to make a profit.

At least 20 students must be enrolled in the class for the instructor to make $1,000 (or more) profit per month.

Explanation:

The function
`f(x)=70n -400` models the profit of the instructor of a guitar class per month.

1. If the instructor makes a profit, then

`f(x)>0\\ \\70n-400>0\\ \\7n-40>0\\ \\7n>40\\ \\n>(40)/(7)\\ \\n>5(5)/(7)`

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

2. If the instructor needs to make 1,000.00 profit per month, then

`f(x)\ge 1,000\\ \\70n-400\ge 1,000\\ \\7n-40\ge 100\\ \\7n\ge 140\\ \\n\ge (140)/(7)\\ \\n\ge 20`

So, at least 20 students must be enrolled in the class for the instructor to make $1,000 (or more) profit per month.