I have two groups of technicians I need to distribute a total number of service tickets to. The total number of techs is 17, with 10 being "normal" techs, and 7 being "specialized" techs. The 7 specialized techs only get assigned half of the amount of tickets the normal techs are assigned, so if the normal group was assigned 20 tickets each the specialized group would have 10 each. Right now I have 194 tickets to be distributed between the two groups. I feel like there is an extremely simple formula to achieve this but I cannot figure it out. Thanks.
I may end up deleting this answer, but I couldn't follow @Marcucciboy's leap of intuition.
Surely the equation you are trying to solve is
10n + 7s = 194
where n is the normal amount of tickets and s the special amount of tickets.
But s=n/2, so you have
10n + 3.5n = 194
which gives you n=14 and s=7 with a few left over.
To check this back, the total number of tickets is 10 * 14 + 7 * 7 = 189 which is about as close as you can get.