Puzzle #214: Cookies

Allan, Bobby, and Tammy each have some cookies. Bobby has two fewer than twice as many as Allan has. Tammy has six more cookies than Allan has. They got those cookies by splitting up a package of twenty-four cookies.

How many cookies does each 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, July 12, 2017 at noon Pacific Time. I will post the answer shortly after.