Question

Lindsey collected 2/3 of a bin of glass bottles to recycle. Diane collected 7 times as many bins as Lindsey. How many bins of bottles did Diane collect?

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

Answer 1

Let \( x \) be the number of bins of glass bottles Lindsey collected. According to the problem, Lindsey collected \( \frac{2}{3} \) of a bin of glass bottles. Thus, we have:

\[
x = \frac{2}{3}
\]

Diane collected 7 times as many bins as Lindsey, so we calculate the amount Diane collected as follows:

\[
\text{Diane's bins} = 7 \times x
\]

Substituting \( x \):

\[
\text{Diane's bins} = 7 \times \frac{2}{3}
\]

To perform the multiplication:

\[
\text{Diane's bins} = \frac{7 \times 2}{3} = \frac{14}{3}
\]

Thus, the number of bins of bottles that Diane collected is

\[
\boxed{\frac{14}{3}}
\]

This can also be expressed as a mixed number:

\[
\frac{14}{3} = 4 \frac{2}{3}
\]

So Diane collected \( 4 \frac{2}{3} \) bins as well. Either \( \frac{14}{3} \) or \( 4 \frac{2}{3} \) is a valid answer.