Valentine’s Day is well over, and the local candy store is clearing out the last of the Valentine’s Day candy. There are some packages of chocolate hearts; candy cinnamon hearts; chocolate-foil roses; and pink, red, and white jelly beans remaining with a total of 40 packages of the four item types. The number of packages of each of the item types is prime and unique. There are fewer packages of the jelly beans than any other item type and more packages of chocolate hearts than of chocolate roses. The packages are split evenly between chocolate and non-chocolate items. How many packages are there of each item?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, March 9, 2016 at noon Pacific Time. I will post the answer shortly after.