How can you put 0.67 with the 6 repeating into a fraction

Write an explicit formula that represents the sequence defined by the following recursive formula:

How many bananas are in a fruit bowl that has 200 total apples and bananas if there are 31 bananas for every 93 apples

Damon makes 20 cups of lemonade by mixing lemon juice and water. the ratio of lemon juice to water is shown in the tape diagram. lemon juice\text{lemon juice} lemon juice water\text{water} water how much lemon juice did damon use in the lemonade? cups