1. [20] Each person in Cambridge drinks a (possibly different) 12 ounce mixture of water and apple juice, where each drink has a positive amount of both liquids. Marc McGovern, the mayor of Cambridge, drinks $\frac{1}{6}$ of the total amount of water drunk and $\frac{1}{8}$ of the total amount of apple juice drunk. How many people are in Cambridge?
Answer:
7
The total amount of liquid drunk must be more than 6 times of the amount that Marc drinks but less than 8 times of the amount that Marc drinks. Therefore, the number of people in Cambridge is more than 6 but less than 8 , so it must be 7 .