## 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?

## Answer Submission Is Not Available

Form is valid through February 2016

## Solution

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!

Here is my solution: If

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 4*a*(*n*- 6) = 3*s*(8 - n).*n* should be natural, so the only possibility is *n* = 7.

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