Question

The present age of Geetha is 1/3 of the present age of her mother. After 5 years, sum of their ages will be 46. Form a linear equation in one variable to find the present ages of Geetha and her mother. What are Geetha's and her mother's ages? * 3​

Answer 1

⇝ Given :-

• The present age of Geetha is 1/3 of the present age of her mother

• After 5 years, sum of their ages will be 46.

⇝ To Find :-

• Their Present Ages by forming linear equation in one variable.

⇝ Solution :-

As The present age of Geetha is 1/3 of the present age of her mother

Let,

• Present Age of Mother = $\rm{3x}$ years

Therefore,

• Present Age of Geetha = $\rm{x}$ years

❒ After Five Years :

• Age of Mother = $\rm{(3x+5)}$ years

• Age of Geetha = $\rm{(x+5)}$ years

⏩ According To Question :

$\red{\text{Age of Geetha + Age of Mother = 46}}$

$:\longmapsto \rm (3x + 5) + (x + 5) = 46$

$\large \bf:\longmapsto \underbrace{ \underline{ 4x + 10 = 46} }$

This is a linear equation in one variable,

⏩ Solving Further :

$:\longmapsto \rm 4x = 46 - 10$

$:\longmapsto \rm 4x = 36$

$:\longmapsto \rm x = \cancel \frac{36}{4}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 9} }}}$

Hence,

Mother's Present Age = $\rm{3x}$ = 27 years

Geetha's Present Age = $\rm{x}$ = 9 years

$\small\pink{\begin{cases} \bf Geetha's\:Present\:Age = 9 \:years \\  \\  \bf Mother's\:Present\:Age = 27 \: years\end{cases}}$

Answer 2

Given :-

The present age of Geetha is 1/3 of the present age of her mother. After 5 years, sum of their ages will be 46

To Find :-

What are Geetha's and her mother's ages

Solution :-

Let the age of her mother be m

Age of Geetha = m/3

After 5 years

Age of mother = m + 5

Age of Geetha = m/3 + 5

${\large{\bf{\underline{\underline{\dag \; Part \; I :-}}}}}$

m/3 + 5 + m + 5 = 46

${\large{\bf{\underline{\underline{\dag \; Part \; II :-}}}}}$

m/3 + 5 + m + 5 = 46

m + 15 + 3m + 15/3 = 46

4m + 30/3 = 46

4m + 30 = 3(46)

4m + 30 = 138

4m = 138 - 30

4m = 108

m = 108/4

m = 27

Now

Age of Geetha = 1/3 × m

Age of Geetha = 1/3 × 27

Age of Geetha = 9 years