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

x^{2} + 3x – 40 = 30

x^{2} + 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

x^{2} + 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

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