How many boxes in total?

Let's work through this backwards, starting with $13$ red boxes and adding green and blue boxes. We have $13$ empty boxes and $13$ boxes total. First, let's add $7$ blue boxes to a red box (because that is the only thing we can do). We now have a total of $20$ boxes total (because we added $7$ ), but when we added the blue boxes, one of the red boxes became full. Therefore, we only added $6$ empty boxes (or rather, we added $7$ empty boxes and filled $1$ other, so there was a net of $6$ added empty boxes). In fact, every time you add $7$ boxes to any box, you add $7$ boxes total and $6$ empty boxes total. So, after $n$ times, the total of boxes will be $13+7n$ , while the total of empty boxes will be $13+6n$ .

Now, we are given that $13+6n=145$ . This can be solved to find that $n=22$ . Plugging this into $13+7n$ to find the total number of boxes, we find that there are $167$ total boxes.