Question

Form the pair of linear equations for the following problem and find their solution by substitution method.

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Answer 1

Let present age of Jacob = x year

And present Age of his son is = y year

Five years hence,

Age of Jacob will = x + 5 year

Age of his son will = y + 5 year

Given that the age of Jacob will be three times that of his son

x + 5 = 3(y + 5)

Adding 5 both side, we get

x = 3y + 15 - 5

x = 3y + 10           ...(i)

Five years ago,

Age of Jacob will = x - 5 year

Age of his son will = y - 5 year

Jacob’s age was seven times that of his son

x – 5 = 7(y -5)

⇒ x - 5 = 7y - 35

⇒ x - 5 = 7y - 35

⇒ x - 7y = -30         ...(ii)

Putting the value of x from equation (ii) we get

x - 7y = -30

⇒ x = 7y – 30

Now on substituting the value of x in equation (i)

x - 3y = 10

⇒ 7y – 30 – 3y = 10

⇒ 4y = 10 + 30

⇒ 4y = 40

⇒ y = 10

Putting y = 10 in equation (ii)

⇒ x = 7(10) – 30

⇒ x = 70 – 30

= 40

Hence, the Present age of Jacob is 40 years and the present age of his son is 10 years.