Question

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

Answer 1

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

Explanation:

Then
`n*(n+5)=24->n^2+5n=24->`

Everything to one side:
`n^2+5n-24=0->` factorise:
`(n+8)(n-3)=0->n=-8orn=3`

`n=3` is the only positive solution, so the numbers are:
`3and8`

Extra :
You could also have done this by factoring `24` and note the differences:
`24=1*24=2*12=3*8=4*6`
where only `3and8` give a difference of `5`