present age of seema's mother is 5 time and 1 year more then seema .fo

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

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»

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,

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