Alright, let's solve this problem step by step. We have 1003 and 7095 and we're adding them together.

Step 1: We'll start by adding the digits 3 & 5 in column 1 and get 8.

Step 2: We'll start by adding the digits 0 & 9 in column 2 and get 9.

Step 3: We'll start by adding the digits 0 & 0 in column 3 and get 0.

Step 4: We'll start by adding the digits 1 & 7 in column 4 and get 8.

So, 1003 + 7095 = 8098.

