Let the amount of glass bottles that Manuel collected be \( x \). According to the problem, Manuel collected \( \frac{1}{4} \) of a bin of glass bottles, so \( x = \frac{1}{4} \).
Jennifer collected \( 8 \frac{1}{2} \) times as many bins as Manuel. First, we convert \( 8 \frac{1}{2} \) to an improper fraction:
\[ 8 \frac{1}{2} = 8 + \frac{1}{2} = 8 + 0.5 = 8.5 = \frac{17}{2} \]
Now, we can calculate how many bins Jennifer collected:
\[ \text{Bins Jennifer collected} = \left(\frac{17}{2}\right) \times \left(\frac{1}{4}\right) \]
To multiply these fractions:
\[ \text{Bins Jennifer collected} = \frac{17 \times 1}{2 \times 4} = \frac{17}{8} \]
Thus, the number of bins of bottles Jennifer collected is:
\[ \frac{17}{8} \]
To express this as a mixed number:
\[ \frac{17}{8} = 2 \frac{1}{8} \]
So the final answer is that Jennifer collected:
\[ \boxed{\frac{17}{8}} \text{ bins or } 2 \frac{1}{8} \text{ bins.} \]
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