Question

present age of seema's mother is 5 time and 1 year more then seema .four year before product of thire ages are 22 then find thire present age​

Answer 1

Basic Concept Used :-

Writing Systems of Linear Equations from Word Problems

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.

Let's solve the problem now!!

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

• Let present age of Seema be 'x' years

So,

• Mother's present age be 5x + 1 years

So, we have present ages of two as

$\begin{gathered}\begin{gathered}\bf \:Age \:of-\begin{cases} &\sf{Seema = x \: years} \\ &\sf{Mother \: = 5x + 1 \: years} \end{cases}\end{gathered}\end{gathered}$

Now,

• 4 years ago, the ages are as follow :-

$\begin{gathered}\begin{gathered}\bf \:Age \:of-\begin{cases} &\sf{Seema = x - 4\: years} \\ &\sf{Mother \: = 5x + 1 - 4 = 5x - 3 \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement,

• The product of their ages 4 years ago is 22.

$\rm :\longmapsto\:(5x - 3)(x - 4) = 22$

$\rm :\longmapsto\: {5x}^{2} - 20x - 3x + 12 = 22$

$\rm :\longmapsto\: {5x}^{2} - 23x - 10 = 0$

$\rm :\longmapsto\: {5x}^{2} - 25x + 2x - 10 = 0$

$\rm :\longmapsto\:5x(x - 5) - 2(x - 5) = 0$

$\rm :\longmapsto\:(x - 5)(5x - 2) = 0$

$\rm :\implies\:x = 5 \: \: \: or \: \: \: x = \dfrac{2}{5} \: \{rejected \}$

Hence,

$\begin{gathered}\begin{gathered}\bf \:Age \:of-\begin{cases} &\sf{Seema = x = 5\: years} \\ &\sf{Mother \: = 5x + 1 = 5 \times 5 + 1 = 26\: years} \end{cases}\end{gathered}\end{gathered}$