Question

A man is 25 years older than his son. After 10 years he will be twice the age of his son . Find their present ages.

Answer 1

Step-by-step explanation:

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Answer 2

The present age of the man is 40 years and his son is 15 years.

Given :

The age of man is 25 years more than his son

The age of man is twice his son after 10 years

To Find :

The current age of the Man and his son in the word problem

Solution :

Let the current age of the Man be "x" and the current age of his son be "y".

It is given that the man is 25 years older than his son. So, we can form the equation from it.

Equation 1 :    $x = 25 + y$

Also, it is said that the man was double the age of his son 10 years after. The age of the man and his son 10 years later will be "x+10" and "y+10" respectively. Thus, we can form another equation from it.

Equation 2 :        $( x +10) = 2 * (y+10)$

                              $x + 10 = 2y + 20$

                              $x - 2y = 20 - 10$

                              $x - 2y = 10$

We solve the system of two equations using the Substitution method i.e. substitute x with the value from equation 1 i.e. "25+y" in equation 2 :

                  $(25+y) - 2y = 10$

                   $25 + y - 2y = 10$

                          $25 - y = 10$

                                 $y = 25 - 10$

                                 $y = 15$

Subsituing "y" to find "x" :

                              $x = y + 25$

                                 $= 25+15$

                                 $= 40$

Hence, the current age of the man and his son is 40 and 15 years respectively.

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