Question

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer?

Answer 1

Lets call our integers:
x, x+1 and x+2

the product of the smaller two integers is 5 less than 5 times the largest integer: this means
x*(x+1) +5= (x+2)*5

taking things out of the brackets:

x*x+x+5= 5x+10

putting everything on one side:

x*x+x -5x +5-10= 0

calculating:

x*x+-4x -5= 0

we can put it into brackets:

(x+1)*(x-5)=0

So we have x=-1 (which can't be, it has to be positive)
or x=5, which is the answer!