Final answer:
The problem is a system of equations, where the two numbers involved are represented by x (smaller number) and y (larger number). By substituting and simplifying the equations, we find that the smaller number is 4 and the larger number is 12.
Step-by-step explanation:
The question involves a system of equations. Let's assume the smaller number is x and the larger number is y. According to the problem, we have two equations: y = 2x + 4 (the larger number is 4 more than twice the smaller number) and x + y = 2(y - x) (the sum of two numbers is twice their difference).
First, we can substitute the expression from the first equation into the second one: x + (2x + 4) = 2((2x + 4) - x). Simplifying this, we get x + 2x + 4 = 4x + 8 - 2x, which results in 3x + 4 = 2x + 8. Solving for x, we find that x = 4.
Now, plugging x = 4 back into the first equation, we get y = 2(4) + 4, so y = 12. Therefore, the smaller number is 4 and the larger number is 12.