Question

What are three consecutive odd positive integers such that three times the sum of all three is 152 less than the product of the first and second integers?

Answer 1

Numbers are `17,19` and `21`.

Explanation:

Let the three consecutive odd positive integers be `x,x+2` and `x+4`

three times their sum is `3(x+x+2+x+4)=9x+18`

and product of first and second integers is `x(x+2)`

as former is `152` less than the latter

`x(x+2)-152=9x+18`

or `x^2+2x-9x-18-152=0`

or `x^2-7x+170=0`

or `(x-17)(x+10)=0`

and `x=17` or`-10`

as numbers are positive, they are `17,19` and `21`