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?

Question

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

$$\boxed{{\displaystyle \frac{14}{3}}}$$

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.