Question

Total expenses of running Sanskar Velly School which is a day boarding school are partly fixed and partly
students?varying linearly with the number of students. The average expense per student is $70 when there are 25
students and $60 when there are 50 students. What is the average expense per student when there are
100 ​

Answer 1

SOLUTION

GIVEN

Total expenses of running Sanskar Velly School which is a day boarding school are partly fixed and partly

students varying linearly with the number of students. The average expense per student is $ 70 when there are 25 students and $ 60 when there are 50 students.

TO DETERMINE

The average expense per student when there are 100 students

EVALUATION

Let the fixed amount is $ x and varying amount per student be $ y

Now it is given that the average expense per student is $ 70 when there are 25 students

$\displaystyle \sf{ \frac{x + 25y}{25} = 70 }$

∴ x + 25y = 1750 - - - - - - - - - (1)

Again the average expense per student is $ 60 when there are 50 students

$\displaystyle \sf{ \frac{x + 50y}{50} = 60 }$

∴ x + 50y = 3000 - - - - - - - - - (2)

Equation (2) - Equation (1) gives

25y = 1250

∴ y = 50

From Equation (1) we get

x = 1750 - 25y

$\implies \sf{x = 1750 - (25 \times 50)}$

$\implies \sf{x = 1750 -1250}$

$\implies \sf{x = 500}$

∴ The average expense per student when there are 100 students

$\displaystyle \sf{ = \frac{x + 100y}{100} }$

$\displaystyle \sf{ = \frac{500 + (100 \times 50)}{100} }$

$\displaystyle \sf{ = \frac{500 + 5000}{100} }$

$\displaystyle \sf{ = \frac{ 5500}{100} }$

$\displaystyle \sf{ =55 }$

FINAL ANSWER

The average expense per student when there are 100 students = $ 55

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