Question

Write the quadratic equation for the following:“The age of Ruchi is twice the age of Monika. The

product of their ages will be 160 after four years. Find their present ages.”​

Answer 1

ANSWER:

According to Problem:

Let the age of Monika be x years.

and, Ruchi's age will be 2x years.

Now,

Monika's age after 4 years = x + 4

And Ruchi's age after 4 years = 2x + 4

ATQ,

Product of their ages is 160 after 4 years.

= $(x + 4) (2x + 4) = 160$

= $x(2x + 4) + 4(2x + 4) = 160$

= $2 {x}^{2} + 4x+ 8x + 16 = 160$

= $2 {x}^{2} + 12x + 16 = 160$

Divide this quadratic equation by 2

${x}^{2} + 6x + 8 = 80$

By solving this equation:

= ${x}^{2} + 6x + 8 = 80$

= ${x}^{2} + 6x + 8 - 80 = 0$

= ${x}^{2} + 6x - 72 = 0$

= ${x}^{2} + (12 - 6)x - 72 = 0$

= ${x}^{2} + 12x - 6x - 72 = 0$

= $x(x + 12) - 6(x + 12) = 0$

= $(x - 6)(x + 12) = 0$

= $(x - 6) = 0 \: or \: (x + 12) = 0$

= $x = 6 \: or \: x = - 12$

Note: As age cannot be negative, ignore the negative value and take x as 6.

Hence,

Monika's present age = x = 6 years.

Ruchi's present age = 2x = 2 × 6 = 12 years.

___________________________

Answered By : MoonGurl01

Answer 2

Given :    The age of Ruchi is twice the age of Monika. The  product of their ages will be 160 after four years.

To find : Write the quadratic equation . Find their present ages

Solution:

Let say age of monika  = M  Years

The age of Ruchi is twice the age of Monika.

=> Age of Ruchi  = 2 M  Years

The  product of their ages will be 160 after four years

After 4 years Monika Age = M + 4 years

After 4 years Ruchi age = 2M + 4  Years

Products of age = (M + 4)(2M + 4)  

(M + 4)(2M + 4)    = 160

=> 2M²  + 12M + 16 = 160

=> M² + 6M + 8 = 80

=> M² + 6M - 72 = 0

M² + 6M - 72 = 0  is the required quadratic equation

M² + 6M - 72 = 0

=> M²+ 12M  - 6M - 72 = 0

=> M (M + 12) - 6(M + 12) = 0

=> (M - 6)(M + 12) = 0

=> M = 6     ( M = - 12 not possible as age can not be negative )

Monika Age = 6 Years

Ruchi Age = 12 years

M² + 6M - 72 = 0  is the required quadratic equation

Learn More:

the combined age of joshi and jonny is 49 joshi is twice as old as ...

https://brainly.in/question/13949967

Shikha is 3 years younger than ravish if the sum of their ages is 37 ...

https://brainly.in/question/7599061

three years ago aman age was 11 times his son age . nine year ...

https://brainly.in/question/9436824