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10 grade maths> . Represent the following situations in t...

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. Represent the following situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Pawan Prajapati , 5 Years ago

Grade 12

3 Answers

Harshit Singh

Last Activity: 5 Years ago

Dear student

Let us consider,
Age of Rohan’s = x years
Therefore, as per the given question,
Rohan’s mother’s age = x + 26
After 3 years, Age of Rohan’s = x + 3
Age of Rohan’s mother will be = x + 26 + 3
= x + 29
The product of their ages after 3 years will be equal to 360,
such that (x + 3)(x + 29) = 360
⇒ x^2 + 29x + 3x + 87 = 360
x^2 +32x+87=360

Thanks

KRIPA SHANKAR DWIVEDI

Last Activity: 4 Years ago

Let rohans age=X

Rohans mother age=X+26

after 3 years

Rohan age=X+3

Rohan’s mother age=(X+26)+3=X+29

NOW A.T.Q

Product of age after 3 years=360

(X+3)(X+29)=360

X(X+29)+3(X+29)=360

^{X^2+29X+3X+87=360}

^{X^2+32X+87−360=0}

^{X^2+32X-272=0}

^{It’s the form of}

^{ax^2+bx+c=0}

^{where a=1 b=32 c=−273}

^{hence it’s a quadratic equation}

Ram Kushwah

Last Activity: 4 Years ago

Let the age of Rohan=x years

AS mother is 26 older than Rohan

so Mother’s age=x+26

Now the product of their ages after 3 year will be 360

so (x+3)(x+3+26)=360

(x+3)(x+29)=360

x²+29x +3x +87=360

x²+32x-360+87=0

x²+32x-273=0

This is the quadratic equation formed

To find Rohan’s age:

x²+32x-273=0

x²+39x-7x-273=0

x(x+39)-7(x+39)=0

(x+39)(x-7)=0

x= -39 or 7

Age can not be negative

So Rohan’s age= 7 years

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