Final answer:
The correct equation to represent the product of two consecutive positive integers being 36 more than six times the first one is x(x + 1) = 6x + 36, which is option D.
Step-by-step explanation:
The question asks us to determine which equation would be used to solve the word problem about two consecutive positive integers whose product is 36 more than six times the first integer. Since we're working with consecutive integers, we can represent them as x (the first integer) and x + 1 (the second integer, which is one more than the first). The product of these two integers would be x(x + 1).
The word problem states that their product is 36 more than six times the first integer, which translates to x(x + 1) = 6x + 36. Therefore, the correct equation that represents this scenario is option D: x(x + 1) = 6x + 36.