The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30. Find her present age.
Let the present age of Tanvy be x years
Tanvy’s age five years ago = (x – 5) years
Tanvy’s age eight years from now = (x + 8) years
(x – 5)(x + 8) = 30
x2 + 3x – 40 = 30
x2 + 3x – 70 = 0
Using the splitting middle term – the middle term of the general equation is divided in two such values that:
Product = a.c
For the given equation a = 1 b = 3 c = – 70
= 1. – 70 = – 70
And either of their sum or difference = b
= 3
Thus the two terms are 10 and – 7
Difference = 10 – 7 = 3
Product = 10. – 7 = – 70
x2 + 10x – 7x – 70 = 0
x (x + 10) – 7(x + 10) = 0
(x + 10) (x – 7) = 0
x = – 10 or x = 7 (age cannot be negative)
x = 7
The present age of Tanvy is 7 years