If m and n are two positive integers such that 7m + 11n = 200, then the minimum possible value of m + n is

$$7m + 11n = 200$$

It is given that both m and n are positive integers. We need to find one integer pairs of (m,n) that satisfy the equation for these questions. 

If we put the value of n = 1, then the value of m = 27. Thus, one solution will be (27,1).

Now, to find the next solution of n, we need to add the coefficient of m in the original value of n, and to find the next value of m, we need to subtract the coefficient of n in the original value of m. (One should be added, the other should be subtracted. Since we need the positive values of m and n, thus we are adding in n, and subtracting from m). We will continue this process till we get any value of m or n as negative. 

Thus, the other solutions of these equations will be - (m,n) = (16,8), (5,15)

If (m,n) = (27,1) => m+n = 28.

If (m,n) = (16,8) => m+n = 24.

If (m,n) = (5,15) => m+n = 20.

Thus, the minimum value of m + n = 20.