Question

Rajni’s mother is 36 years old. She is 6 years older than three times Rajni’s age. Write an equation to find the age of Rajni’s mother. (Take Rajni’s age to be n years)

Answer 1

Hint: We assume Rajni’s age as a variable. Form an equation for the age of Rajni’s mother whose present age is given in numeral form. Use the meaning of the word older to add the given number of years and meaning of the word thrice to write the relation between age of Rajni and her mother.

Complete step-by-step answer:
We are given that the age of Rajni’s mother is 36 years. … (1)
Let us assume the age of Rajni as ‘n’ years.
We are given in the question that her mother is 6 years older than three times Rajni’s age
We know three times Rajni’s age will be written as \[3n\].
Now since her mother is is 6 years older than three times Rajni’s age, we will add 6 to \[3n\]
The age of Rajni’s mother will be \[3n + 6\] … (2)
Now we equate the age of Rajni’s mother from equations (1) and (2)
\[ \Rightarrow 3n + 6 = 36\]
Shift all constant values to right hand side of the equation
\[ \Rightarrow 3n = 36 - 6\]
Calculate the difference on right hand side of the equation
\[ \Rightarrow 3n = 30\]
Cancel same factors i.e. 3 from both sides of the equation
\[ \Rightarrow n = 10\]
So, the age of Rajni is 10 years.

\[\therefore \]Equation to find Rajni’s age is \[3n + 6 = 36\], where n is Rajni’s age. Also, the age of Rajni is 10 years.

Note:
Many students make the mistake of writing the equation wrong as they get confused with whose age is the word ‘she’ referring to. Keep in mind in a mother daughter relationship, mother would always be the older one and the daughter will always be the younger one, so the equation is formed for the mother.