# The product of two consecutive integers is 80 more than 15 times the larger integer. What are the integers?

Jun 1, 2016

$19 , 20$ or $- 5 , - 4$

#### Explanation:

Let the larger integer be $n$.

Then we are told:

$\left(n - 1\right) n = 15 n + 80$

Subtract $15 n$ from both sides to get:

$\left(n - 16\right) n = 80$

So we are looking for a pair of factors of $80$ which differ by $16$.

The pair $20 , 4$ works.

Hence $n = 20$ or $n = - 4$

So the two consecutive integers are $19 , 20$ or $- 5 , - 4$