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?
(USE WITHOUT CALCULATOR)

Answer 1

Let's say the first number is "a"
the next consecutive can just be "a+1" and  the next, you guessed it, "a+2"
the two smaller ones are a and a+1, the larger one is a+2

now, the product of "a" and "a+1" equals 5 times "a+2" but less by 5

thus   a(a + 1) = 5(a + 2) - 5   <----- solve for "a"