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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.

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    @André Nicolas:I know,but sometimes it's $f$orm$a$l to give the $a$nswer as the pro$b$lem is not st$a$ted properly.Th$a$nks for the inputs :-)2011-08-21

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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 $b$).

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    It's not much o$f $a stretch to interpret "varying with the number of students" as "varying directly with the number of students," which is another way to say "proportional to the number of students." And if you don't make some stretch, there's no way to solve the problem, so presumably this is what was intended.2011-08-21