Question

The product of two positive consecutive numbers is 42. What is the smaller number?

Answer 1

X = first integer, y = second integer (right after x)

since y is right after x, we can say
y = x+1

If the product of the two integers (x and y) is 42, then
x*y = 42
x*( y ) = 42
x*( x+1 ) = 42 ... y is replaced with x+1
x*x + x*1 = 42
x^2 + x = 42
x^2 + x - 42 = 0
(x + 7)(x - 6) = 0 ... factor
x + 7 = 0 or x - 6 = 0
x = -7 or x = 6

The result must be positive as the problem states it, so we toss out x = -7
The only answer is x = 6

If x = 6, then
y = x+1
y = 6+1
y = 7

The two consecutive numbers are 6 and 7

The final answer is 6

Sure enough, 6*7 = 42 checks out