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

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Answer 1 · 2016-06-01T23:41:42

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

Let the larger integer be $n$ $n$ .

Then we are told:

$(n - 1) n = 15 n + 80$ $(n-1)n = 15n+80$

Subtract $15 n$ $15n$ from both sides to get:

$(n - 16) n = 80$ $(n-16)n = 80$

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

The pair $20, 4$ $20, 4$ works.

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

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