To find out how many bins of bottles Mitch collected, we start with the amount Edgar collected, which is \( \frac{1}{2} \) of a bin.
Next, we need to calculate how many bins Mitch collected, which is \( 6 \frac{1}{5} \) times the amount Edgar collected.
First, we need to convert \( 6 \frac{1}{5} \) to an improper fraction.
\[ 6 \frac{1}{5} = 6 + \frac{1}{5} = \frac{30}{5} + \frac{1}{5} = \frac{31}{5} \]
Now we multiply this by the amount of bins Edgar collected, which is \( \frac{1}{2} \).
\[ \text{Bins collected by Mitch} = \frac{31}{5} \times \frac{1}{2} \]
To multiply these two fractions, we multiply the numerators and then the denominators:
\[ \frac{31 \times 1}{5 \times 2} = \frac{31}{10} \]
Now, we can convert \( \frac{31}{10} \) to a mixed number if necessary:
\[ 31 \div 10 = 3 \quad \text{(whole number)}\quad \text{ with a remainder of } ,1. \] Thus, we can express \( \frac{31}{10} \) as:
\[ 3 \frac{1}{10} \]
So, the total number of bins of bottles that Mitch collected is
\[ \boxed{\frac{31}{10}} \quad \text{or} \quad \boxed{3 \frac{1}{10}}. \]
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