Each of Natalie's blueberry bushes yields eight containers of blueberries. If she can trade five containers of blueberries for two zucchinis, how many bushes does Natalie need to pick in order to have forty-eight zucchinis?
We know the following two equations: \begin{align*}
1\text{ bush} &= 8\text{ containers}\\
5\text{ containers} &= 2\text{ zucchinis}.
\end{align*} To find the value of 48 zucchinis in terms of bushes, we multiply by fractions equal to 1 where the numerator and denominator are in different units, canceling units as we go. Thus, we set up the following equation to find our answer: $48\text{ zucchinis} = 48\text{ zucchinis}\times \frac{5\text{ containers}}{2\text{ zucchinis}}\times\frac{1 \text{ bush}}{8\text{ containers}}=\boxed{15} \text{ bushes}$.
15
Level 2
Algebra
Problem: Each of Natalie's blueberry bushes yields eight containers of blueberries. If she can trade five containers of blueberries for two zucchinis, how many bushes does Natalie need to pick in order to have forty-eight zucchinis?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine how many bushes Natalie needs to pick, we first need to calculate how many containers of blueberries are required to obtain forty-eight zucchinis. Since five containers yield two zucchinis, we can find the number of containers needed for one zucchini by dividing the number of containers by the number of zucchinis: 

5 containers / 2 zucchinis = 2.5 containers per zucchini.

Next, we multiply the number of zucchinis desired by the number of containers needed for one zucchini:

48 zucchinis * 2.5 containers per zucchini = 120 containers.

Now, we know that each blueberry bush yields eight containers of blueberries. To find out how many bushes are needed to produce 120 containers, we divide the total number of containers by the yield per bush:

120 containers / 8 containers per bush = 15 bushes.

Thus, Natalie needs to pick 15 bushes to obtain enough blueberries for forty-eight zucchinis. The final answer is 15.<|END_OF_LATENT|> The final answer is $15$.