Question

Femina’s mother is 22 years younger than Femina’s grandmother
and 27 years older than Femina.The sum of their ages are 121 years.
Find their present ages.

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Femina’s mother is 22 years younger than Femina’s grandmother.

• Femina's mother 27 years older than Femina.

So,

$\begin{gathered}\begin{gathered}\sf\: Given-\begin{cases} &\sf{Femina \: present \: age \: be \: x \: years} \\ &\sf{Femina \: mother \: present \: age \: be \: x + 27 \: years}\\ &\sf{Femina \: grandmother \: present \: age \: be \: x + 49 \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement

☆ The sum of their ages be 121 years .

$\rm :\longmapsto\:x + x + 27 + x + 49 = 121$

$\rm :\longmapsto\:3x + 76 = 121$

$\rm :\longmapsto\:3x= 121 - 76$

$\rm :\longmapsto\:3x= 45$

$\bf\implies \:x = 15\: years$

,

$\begin{gathered}\begin{gathered}\sf\: Hence-\begin{cases} &\sf{Femina \: present \: age \: = 15 \: years} \\ &\sf{Femina \: mother \: present \: age = 42\: years}\\ &\sf{Femina \: grandmother \: present \: age = 64 \: years} \end{cases}\end{gathered}\end{gathered}$

Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.