Question

Manuel collected 1/4 of a bin of glass bottles to recycle. Jennifer collected 8 1/2 times as many bins as Manuel. How many bins of bottles did Jennifer collect?

Write your answer as a fraction or as a whole or mixed number.

bins

Answer 1

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:

\[
\boxed{\frac{17}{8}} \text{ bins or } 2 \frac{1}{8} \text{ bins.}
\]