There are two positive number such that sum of twice the first and thrice the second is 39, while the some of thrice the first and twice the second is 36. The larger of the two is ________

Let's denote the two numbers as x and y.

From the problem, we have two equations:

2x + 3y = 39 (equation 1)

3x + 2y = 36 (equation 2)

We can solve these two equations simultaneously to find the values of x and y.

First, let's multiply equation 1 by 2 and equation 2 by 3:

4x + 6y = 78

9x + 6y = 108

Now, let's subtract the first equation from the second:

5x = 30

So, x = 30 / 5 = 6.

Now that we have the value of x, we can substitute it into equation 1 to find the value of y:

2*6 + 3y = 39

12 + 3y = 39

3y = 39 - 12 = 27

So, y = 27 / 3 = 9.

Therefore, the two numbers are 6 and 9, and the larger of the two is 9.