February 2016 Problem

A group of tourists has a lunch. Two different jars of apple juice and of strawberry juice are put on the table.

Each tourist takes a 200-ml glass of fruit cocktail, mixing both juices at random. Jack takes a sixth of the apple juice amount and an eighth of the strawberry juice amount. Every glass contains both juices. How many people are in the group?

Dear visitors, many thanks for your solutions. Many of them were correct, though not always optimal. The first ones to answer correctly were Hyun-Woo, Samson, Clara and Christian. My congratulations!

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    Here is my solution:   If a is the quantity of the apple juice and s - of the strawberry juice, then Jack consumed (a/6+s/8).   Every tourist  had the same glass, so for n tourists, (a/6+s/8)n = a + s. Rearranging, we get                                                                                                                                                                                                                                                                                                    4a(n - 6) = 3s(8 - n).

n should be natural, so the only possibility is n = 7.