How to approach this problem? The problem statement: > The expenses of a tuition class are partly fixed and partly variable with the number of students.The charge is $40\$$ per head when there are $25$ students and $60\$$ per head when there are $50$ students.Find the charge per head when there are $100$ students. I am looking for some hints/ideas about approaching this problem.

If $x$ is the number of students, and $y$ is the tuition costs, you have

$$y = ax + b$$

in which $a$ controls the variable part and $b$ controls the fixed part of the total... if you knew $a$ and $b$ you could calculate the costs for any given number of students. To find them, just use the two known values for $x$ and $y$, which gives you two equations (for your two unknowns $a$ and $b$).