How would you find by using algebra two consecutive odd numbers whose product is 2499?

Let the first odd number be (n - 1), then the second odd number is (n - 1) + 2 = (n + 1)

Then:

(n - 1)(n + 1) = 2499

⇒ n2 - 1 = 2499

⇒ n2 = 2500

⇒ n = 50

⇒ (n - 1) = (50 - 1) = 49

& (n + 1) = (50 + 1) = 51

⇒ the two consecutive odd numbers whose product is 2499 are 49 & 51.