A smoothie recipe calls for 2 cups of juice for every 3 cups of strawberries. How many cups of strawberries would you need for 9 cups of juice?

To solve the problem about the smoothie recipe, let's first establish the relationship between the cups of juice and the cups of strawberries based on the information given.

The recipe states:
- For every 2 cups of juice, you need 3 cups of strawberries.

We can express this relationship with a double number line. Here’s how it would look with the increments based on the given ratio:

| Juice (cups) | Strawberries (cups) |
|--------------|---------------------|
| 0 | 0 |
| 2 | 3 |
| 4 | 6 |
| 6 | 9 |
| 8 | 12 |
| 10 | 15 |

Now, let's answer the question: how many cups of strawberries are needed for 9 cups of juice?

Since the ratio we have is:
- For 2 cups of juice → 3 cups of strawberries

To find the amount of strawberries needed for 9 cups of juice, we’ll set up a proportion based on the recipe's ratio:

\[
\frac{2\, \text{cups of juice}}{3\, \text{cups of strawberries}} = \frac{9\, \text{cups of juice}}{x\, \text{cups of strawberries}}
\]

Cross-multiplying gives:

\[
2x = 3 \times 9
\]

Calculating the right-hand side:

\[
2x = 27
\]

Now, divide both sides by 2:

\[
x = \frac{27}{2} = 13.5
\]

Therefore, you would need **13.5 cups of strawberries** for 9 cups of juice.