Question

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.??​

Answer 1

Answer:

7 years

Step-by-step explanation:

let rohans present age be x

his mothers age=x+26

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

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

x²+32x+87=360

x²+32x-273=0

x²+39x-7x-273=0

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

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

x=-39 or x=7

x cant be-39 as age cant be negative

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∴ rohans current age=7 years

Answer 2

as, rohan's mother is 26 yrs older than him

• let rohan's age be 'x'
• so, rohan's mother's age would be 'x+26'
• After three yrs, rohan's age would be 'x+3'
• Similarly, after three yrs rohan's mother's age would be 'x+26+3' = 'x+29'

Now, we know that

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

multiplying each term of first equation with each term of the other equation we get,

x²+29x+3x+87 = 360

Solving the equation for the value of x, we get

x²+29x+3x+87 =360

x²+32x = 360-87

x³+32x-273 = 0

factorising this equation, we get it's factor by factor theorem we get,

(x-7) (x+32)

taking 'x-7' to find another factor of this equation (u can choose any) we get, it's another factor as 'x+7'

Now as per logic, -7 can't be any age. So, present age of Rohan is 7 yrs

hope it helps.....