Question

Manish’s mother is one more than 5 times his present age. 4

years ago the product of their ages is 220. Find their present

age
​

Answer 1

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

• Manish mother is 1 more than 5 times his present age.

• 4 years ago, the product of their ages is 220.

$\large\underline{\sf{To\:Find - }}$

• Present age of Mother and Manish.

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

Basic Concept Used :-

Writing System of 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!!

• Let present age of Manish be 'x' years.

As, Manish mother is 1 more than 5 times his present age.

So,

• Manish Mother present age be 1 + 5x years.

So, we have

$\begin{gathered}\begin{gathered}\bf \: Present \: age \: of \begin{cases} &\sf{Manish \: = \: x \: years} \\ &\sf{Mother \: = 5x + 1 \: years} \end{cases}\end{gathered}\end{gathered}$

Now, 4 years ago

• Manish age = x - 4 years

and

• Manish mother age = 5x + 1 - 4 = 5x - 3 years.

According to statement, 4 years ago, the product of their ages is 220.

$\bf\implies \:(x - 4)(5x - 3) = 220$

$\rm :\longmapsto\: {5x}^{2} - 3x - 20x + 12 = 220$

$\rm :\longmapsto\:5 {x}^{2} - 23x - 208 = 0$

$\rm :\longmapsto\:x = \dfrac{ - ( - 23) \: \pm \: \sqrt{ {( - 23)}^{2} - 4( -208)(5) } }{2 \times 5}$

$\rm :\longmapsto\:x = \dfrac{23 \: \pm \: \sqrt{529 + 4160} }{10}$

$\rm :\longmapsto\:x = \dfrac{23 \: \pm \: \sqrt{4689} }{10}$

$\rm :\longmapsto\:x \: = \: \dfrac{23 \: \: \pm \: 68.48 }{10}$

$\rm :\longmapsto\:x = \dfrac{23 + 68.48}{10} = \dfrac{91.48}{10} = 9.15 \: years$

Hence,

$\begin{gathered}\begin{gathered}\bf \: Present \: age \: of \begin{cases} &\sf{Manish \: = \: 9.15 \: years} \\ &\sf{Mother \: = 5x + 1 = 46.75 \: years} \end{cases}\end{gathered}\end{gathered}$

Answer 2

Answer:

There is a error in your question, product of their age is 22 not 220.

Let Manish age be x.

therefore his mother's age will be 5x+1

.....by the given condition

According to the condition given

$(x - 4)(5x + 1 - 4) = 22$

...by the given condition

$(x - 4)(5x - 3) = 22 \\ = 5 {x}^{2} - 3x - 20x + 12 = 22 \\ = 5 {x}^{2} - 23x + 12 - 22 = 0 \\ = 5 {x}^{2} - 23x - 10 = 0 \\ = 5 {x}^{2} - 25x + 2x - 10 = 0 \\ = 5x(x - 5) + 2(x - 5) = 0 \\ = (5x + 2)(x - 5) = 0$

therefore, here

$5x + 2 = 0 \: \: or \: \: x - 5 = 0 \\ x = - \frac{2}{5} \: \: or \: \: x = 5$

age cannot be negetive.

Therefore Mainsh's age is 5yrs.

And his mother's age is 5x+1= 5× 5 + 1= 25+1 =26

hope it will be helpful

Mark me brainliest.