Final answer:
To find the two numbers, we can set up equations based on the given information and solve them. The first equation represents one positive number being 3 more than twice another, and the second equation represents their product being 27.
Step-by-step explanation:
Let's assume the two numbers are x and y.
According to the given information, one positive number is 3 more than twice another. So we can write this as an equation:
x = 2y + 3
Their product is 27. So we can write this as another equation:
xy = 27
Now, we can substitute the value of x from the first equation into the second equation:
(2y + 3)y = 27
Expanding and simplifying, we get:
2y^2 + 3y - 27 = 0
Now, we can solve this quadratic equation for y. Once we find the value of y, we can substitute it back into the first equation to find the value of x.