Struggling through an AMC 8 problem

My younger son has been practicing for the AMC 8. This week we’ll be going over a few problems here and there that give him trouble. The problem from the practice test today was #16 from the 2016 AMC 8:

Problem 16

This problem really gave him some trouble – as you’ll see from his 5 min struggle below:

I was caught a bit by surprise over the difficulty he was having. It wouldn’t surprise me if the mistakes he was making were quite common mistakes for a problem like this, but I was stuck on what to do. So, I decided to show him one path that leads to the solution to the problem:

So, having shown him one way to solve the problem, I challenged him to find a different solution. Initially he struggled, but then he did something pretty clever:

I definitely struggle to see a good way forward when a problem is giving one of my kids as much trouble as this one was. Hopefully my son was able to see some of the important ideas in the problem after we talked through it in the second video. I really do like the solution he came up with in the third video, though, especially since it is more geometric and less reliant on calculation.