Question

Question 3 (vi)
Form the pair of linear equations for the following problems 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 the age of Jacob be x and the age of his son be y.
According to the given information,
(x + 5) = 3(y + 5)
x - 3y = 10 (1)
(x - 5) = 7(y - 5)
x - 7y = -30 (2)
From (1), we obtain
x = 3y + 10 (3)
Substituting this value in equation (2), we obtain
3y + 10 - 7y = -30
- 4y = -40
y = 10 (4)
Substituting this value in equation (3), we obtain
x = 3 $\times$ 10 + 10
= 40
Hence, the present age of Jacob is 40 years where as the present age of his son is 10 years.