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.
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