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?
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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.