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

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