Question

Express the given information in mathematical form using two variables:
(i) Five years hence a man’s age will be three times his son’s age. The man's age is given by 'x' and his son's age by 'y'.
(ii) One number is 5 more than seven times the other number.

Answer 1

(i) Let the present age of the man and his son be $x$ years and $y$ years respectively.

Five years hence,
Man's age = $(x+5)$ years
Son's age = $(y+5)$ years

According to the question, we have
$x+5=3(y+5)\Rightarrow x+5=3y+15\Rightarrow x-3y=10$
This is a linear equation in two variables which represents the given statement.

(ii) Let the two numbers be $x$ and $y$.
$x=5+7y$
$\Rightarrow x-7y=5$
The equation $x-7y=5$ represents the given statement.