Puzzle #183: Marbles

You have some marbles, each one of the colours red, orange, yellow, green, blue, and violet.

The number of red marbles is twice the number of green marbles. The number of yellow marbles is one-half the number of blue marbles. The number of green marbles is two more than the number of yellow marbles. The number of blue marbles is three less than the number of violet marbles. The number of violet marbles is four more than the number of orange marbles.

If the number of orange marbles is the same as the number of green marbles, how many marbles do you have?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, December 7, 2016 at noon Pacific Time. I will post the answer shortly after.