Salary = f(n students)

Many years ago a teacher’s salary was based on the number of students he had. Suppose a salary of $60 per month was to be paid for 50 students and $50 a month for 30 students. If the actual enrollment was 45 students, what should the teacher be paid?


Show/Hide Solution

Let’s assume the salary formula, f, is a linear function and use the points (50, 60) and (30, 50) to find the equation for f:

We have f = [(60-50)/(50-30]n + b = .5n + b.

Then we substitute (30, 50) to solve for b: 50 = .5(30) + bb = 35.

So f = .5n + 35.

Substituting n = 45, f = .5(45) + 35 = 22.50 + 35 = 57.50.

The teacher should be paid $57.50 per month for 45 students.

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