The sum of the ages of two boys is 18 years. After 6 years, the product of their ages, in years, will be 224. Represent the situation in quadratic form.

Let the age of the younger boy be x. 

The sum of the ages of the two boys is 18 years. 

Therefore, the age of the older boy will be (18 − x). 

It is given that after 6 years, the product of their ages is 224. 

∴(x + 6) (18 − x + 6) = 224 

⇒ (x + 6) (24 − x) = 224 

⇒ 24x − x² + 144 − 6x = 224 

⇒ −x² + 18x + 144 = 224 

⇒ x² − 18x + 80 = 0