Problem D

Boxes of Doughnuts

A bakery is famous for its specialty doughnuts. One weekend they had three flavours available, each packaged in boxes. Peach caramel doughnuts were sold in small boxes with \(3\) doughnuts per box, chocolate fudge doughnuts were sold in medium boxes with \(4\) doughnuts per box, and rainbow doughnuts were sold in large boxes with \(8\) doughnuts per box.

At the end of the weekend, the owner calculated that they sold \(68\) boxes of doughnuts in total. Also an equal number of doughnuts of each flavour were sold. How many doughnuts did they sell in total?