The larger number of 2 numbers is 3 more than twice the smaller. The difference of the larger in the smaller number is 8

x - y = 8

x = 2y + 3

so
2 y + 3 - y = 8

y = 5
x = 5+8 = 13

To solve this problem, we can set up a system of equations.

Let's assume the smaller number is represented by 'x' and the larger number is represented by 'y'.

The problem states that the larger number is 3 more than twice the smaller, so we can write the equation:
y = 2x + 3

The problem also states that the difference between the larger and smaller number is 8, so we can write another equation:
y - x = 8

Now we have a system of two equations:
1) y = 2x + 3
2) y - x = 8

To solve this system of equations, we can use substitution or elimination method. I will use the substitution method in this case.

From equation 1), we can substitute y in equation 2) with its equivalent expression:
2x + 3 - x = 8

Now we can simplify the equation:
x + 3 = 8

Next, we solve for x by isolating the variable:
x = 8 - 3
x = 5

We have found that the smaller number 'x' is equal to 5.

To find the larger number 'y', we substitute the value of x in equation 1):
y = 2(5) + 3
y = 10 + 3
y = 13

Hence, the larger number 'y' is equal to 13.

Therefore, the smaller number is 5 and the larger number is 13.