Question

The product of mothers age five years ago and her age.8 years later is 30.find the present age

Answer 1

Let the present age of mother be x.
five years ago,Her age=x-5
Eight years later,her age=x+8
By question,(x-5)(x+8)=30
or,x^2+3x-40=30
or,x^2+3x-70=0
Solving it,we get x=7.

Answer 2

Let the present age of mother be x


Her age 5 years ago will be x-5

Now her age 8 yeara later will be x+8

According to question,

(x-5)(x+8) = x^2+8x-5x-40

Solving the quadratic equation
x^2+3x-40 = 30

x^2+3x-70=0

Splitting middle term

x^2+10x-7x-70=0

x(x+10)-7(x+10)=0

(x-7)(x+10)=0

So mothers age is 7 years as -10 is not possible