Question

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.​

Answer 1

ATQ A part of the monthly expenses of a family is constant.

Let the constant monthly expense be "x".

Let the expenses on one member in a family be "y".

Given: For a family of 4 persons, the total monthly expenses are ₹10,400.

⇒ Constant expense + Monthly expenses of 4 members = ₹10,400

⇒ x + 4(monthly expense) = ₹10,400

⇒ x + 4y = ₹10,400 ⇔ Eq(1)

Given: for a family of 7 persons, the total monthly expenses are ₹15,800.

⇒ Constant expense + Monthly expenses of 7 members = ₹15,800

⇒ x + 7(monthly expense) = ₹15,800

⇒ x + 7y = ₹15,800 ⇔ Eq(2)

Subtracting Eq(1) from Eq(2) we get:

⇒ x + 7y - (x + 4y) = 15800 - 10400

⇒ x + 7y - x - 4y = 5400

⇒ 3y = 5400

⇒ y = 5400/3

⇒ y = ₹1800

Substitute the value of y, in Eq(1)

⇒ x + 4y = 10400

⇒ x + 4(1800) = 10400

⇒ x + 7200 = 10400

⇒ x = 10400 - 7200

⇒ x = ₹3200

∴ The constant expenses per month (x) = ₹3200

∴ The monthly expenses of each member in the family (y) = ₹1800

Answer 2

Question:

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.

Answer:

The constant expense is ₹3,200/- per month and monthly expenses of each member of the family is ₹1,800

Step-by-step explanation:

Let the constant expense per month of the family be = a

Let the expense per month for a family member be = x

So, now A/Q

For the family of 4 members the total expense is = ₹10,400

= a + 4x = ₹10,400 (equation 1)

The family of 7 people ,the total monthly expense is = ₹15,800

= a + 7x (equation 2)

After subtracting equation 1 from equation 2, we'll get

= a + 7x - (a + 4x) = 15,800 - 10,400

= a + 7x - a - 4x = 5,400

= 3x = 5,400

= x = 5,400 ÷ 3

= x = ₹1,800

Now, after substituting x = 18,000 in equation 1, we'll get

= a + 4x = 10,400

= a + 4 × 1,800 = 10,400

= a + 7,200 = 10,400

= a = 10,400 - 7200

= a = ₹3,200

• Therefore, the constant expense is a = ₹3,200 per month and the monthly expense of each member of the family is x = ₹1,800