Question

A part of monthly expenses of a family is constants and the remaining vary with the number of members in the family. For a family of 4 person, the total monthly expenses are Rs. 10,400 whereas for a family of 7 persons, the total monthly expenses are Rs. 15,800. Find the constant expenses per month and the monthly expenses of each member of a family.

Answer 1

Let x be the constant expense per month of the family,
and y be the expense per month for a single member of the family,

For a family of 4 people,
the total monthly expense is Rs. 10,400.
x + 4y = 10,400                     ...(1)

For a family of 7 people,
the total monthly expense is Rs. 15,800.
x + 7y = 15,800                     ...(2)

Subtracting equation (1) from equation (2),We get :
      x + 7y = 15800
  -  x + 4y = 10400  
     -   -        -           
           3y = 5400
             y = 1800
Substituting y = 1800 in equation (1), We get
x + 4( 1800 ) = 10,400
⇒ x = 3200.

∴ The constant expense is Rs. 3,200 per month and the monthly expense of each member of a family is Rs.1,800.