Mathematics
A part of monthly expenses of a family is constant and the remaining vary with the number of members in the family. For a family of 4 persons, the total monthly expenses are ₹ 10,400; whereas for a family of 7 persons, the total monthly expenses are ₹ 15,800. Find the constant expenses per month and the monthly expenses on each member of a family.
Linear Equations
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Answer
Let constant monthly expense be ₹ x and for each member of the family monthly expense be ₹ y.
Given,
For a family of 4 persons, the total monthly expenses are ₹ 10,400.
⇒ x + 4y = 10400 …….(1)
For a family of 7 persons, the total monthly expenses are ₹ 15,800.
⇒ x + 7y = 15800 …….(2)
Subtracting equation (1) from (2), we get :
⇒ (x + 7y) - (x + 4y) = 15800 - 10400
⇒ x - x + 7y - 4y = 5400
⇒ 3y = 5400
⇒ y = = ₹ 1800.
Substituting value of y in equation (1), we get :
⇒ x + 4(1800) = 10400
⇒ x + 7200 = 10400
⇒ x = 10400 - 7200 = ₹ 3200.
Hence, constant expense = ₹ 3200 and monthly expense = ₹ 1800.
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