Exiles - Apologies. I didn't actually ask for the explanation.
I was simply noting that 3 people did a nice job of explaining their thought process.
Chrome - I knew you understood it. Just got lost towards the end....
BTW
I am on my way to becoming a math teacher ( at the ripe old age of 50 ).
I can assure you that a good teacher respects a variety of approaches
which can yield the same answer.
The issue a teacher faces when a student has an alternate path is the potential
to a) slow down the momentum / process and b) distract / confuse those in the
class who need clarity and the simplest, most direct path.
Unfortunately, the pressure to get through the material can kill the spontaneous
and alternative paths to learning. That's not just a math issue. Sad, but true.