Question

A father's age is three times the sum of the
ages of his two children. After 5 years his age
will be two times the sum of their ages. Find the
present age of the father. (question from linear equation in two variables)​

Answer 1

Given

• Father's age is 3 times the sum of the ages of his 2 children.
• After 5 years his age will be two times the sum of their ages.

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To Find

• The present age of the father.

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Solution

Let's consider the ages of the sons to be 'x' and 'y'.

We know that the age of the father is 3 times the sum of the ages of the two sons. So we can say that the present age of the father is ⇒ 3(x+y) years

After 5 years the ages of the father and sons would be -:

Age of Father ⇒ [3(x + y) + 5] years

Age of Son 1 ⇒ (x + 5) years

Age of Son 2 ⇒ (y + 5) years

With the given data we understand that after 2 years the father's age would be 2 times the sum of their ages. So now we will solve the following equation to find the present age of the father.

⇒ 3(x + y) + 5 = 2(x + 5 + y + 5)

⇒ 3x + 3y + 5 = 2(x + 10 + y)

⇒ 3x + 3y + 5 = 2x + 20 + 2y

⇒ 3x - 2x + 3y + 5 = 20 + 2y

⇒ x + 3y - 2y + 5 = 20

⇒ x + y = 20 - 5

⇒ x + y = 15

We know that the present age of the father is 3(x + y) years. Since we know the value of x + y, we will substitute the values and find the present age of the father.

⇒ 3 (x + y)

⇒ 3 (15)

⇒ 45 years

∴ The present age of the father is 45 years.

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Answer 2

Answer:

Given :-

• A father's age is three times the sum of the
• ages of his two children. After 5 years his age
• will be two times the sum of their ages

To Find :-

Present age of father

Solution :-

Let the sons age be x years and his father age be y years.

Now,

The equation formed

3(x + y)

Now,

After 5 years

Age of father = [3(x + y) + 5]

Age of Son 1 = (x + 5)

Age of Son 2 = (y + 5)

Now,

According to Question after two years father is twice of his son

$\sf 3(x + y) + 5 = 2(x + 5 + y + 5)$

$\sf \: 3x + 3y + 5 = 2x + 10 + 2y + 10$

$\sf \: 3x + 3y + 5 = 2x + 20 + 2y$

$\sf \: 3x - 2x + 3y + 5 = 20 + 2y$

$\sf \: x \: + 3y + 5 = 20 + 2y$

$\sf \: x \: + (3y - 2y) + 5 = 20$

$\sf \: x \: + y + 5 = 20$

$\sf \: x \: + y = 20 - 5$

$\sf \: x + y = 15$

Hence :-

Father's age = 3(x + y)

Father's age = 3(15)

Father's age = 45 years