To find out how much soda Luther and his friends drank in total, we need to add the amounts of lemon-lime soda and cola together.
Luther and his friends drank:
- Lemon-lime soda: \(2 \frac{1}{4}\) bottles
- Cola: \(2\) bottles
First, we convert \(2 \frac{1}{4}\) into an improper fraction: \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]
Now, we convert the 2 bottles of cola into a fraction as well: \[ 2 = \frac{2}{1} = \frac{8}{4} \quad \text{(since we want a common denominator of 4)} \]
Now we can add the two fractions: \[ \frac{9}{4} + \frac{8}{4} = \frac{9 + 8}{4} = \frac{17}{4} \]
This can be converted to a mixed number: \[ \frac{17}{4} = 4 \frac{1}{4} \]
Thus, the total amount of soda they drank is: \[ \boxed{4 \frac{1}{4}} \text{ bottles} \]