# One positive integer is 5 less than another. the product of the two integers is 24, what are the integers?

Jul 5, 2015

Let's call the smallest $n$ and the other one $n + 5$

#### Explanation:

Then
$n \cdot \left(n + 5\right) = 24 \to {n}^{2} + 5 n = 24 \to$

Everything to one side:
${n}^{2} + 5 n - 24 = 0 \to$ factorise:
$\left(n + 8\right) \left(n - 3\right) = 0 \to n = - 8 \mathmr{and} n = 3$

$n = 3$ is the only positive solution, so the numbers are:
$3 \mathmr{and} 8$

Extra :
You could also have done this by factoring $24$ and note the differences:
$24 = 1 \cdot 24 = 2 \cdot 12 = 3 \cdot 8 = 4 \cdot 6$
where only $3 \mathmr{and} 8$ give a difference of $5$