Question

The average age of 3 son and their father is 17. What is the sum of their age?

Answer 1

Answer:

Let the children be ‘a’ and ‘b’ years old, respectively.

Let the mother be ‘m’ years old.

Let the father be ‘f’ years old.

From the question, we know that the father is 36 years old.

=) f = 36

Average = sum of observations / number of observations

Forming equations:

From the first part of the question: The average age of two children and their father is 17years .

=) a+b+f / 3 = 17

Transposing 3 to the other side,

=) a+b+f = 17*3

=) a+b+f = 51

Substituting value of f,

=) a+b+36 = 51

=) a+b = 51–36

=) a+b = 15 - - - - - - - - - - - - - - - (1)

Now, from the second part of the question: The average age of the two children and their mother is 15 years.

=) a+b+m / 3 = 15

Transposing 3 to right hand side,

=) a+b+m = 15*3

=) a+b+m = 45

From equation (1), we know that a+b=15

a+b+m = 45

=) 15+m = 45

=) m = 45–15

=) m = 30

Since ‘m’ was age of mother,

The mother is 30 years old.

Hope it helped you.