To solve this problem using a double number line, we start with the ratio given in the recipe: for every 2 cups of juice, you need 3 cups of strawberries.
First, let's set up our double number line:
Juice (cups) | Strawberries (cups) ------------------------|------------------------ 0 | 0 2 | 3 4 | 6 6 | 9 8 | 12 10 | 15
Now, we can see that for every 2 cups of juice, we know how many cups of strawberries we need.
To find out how many cups of strawberries you would need for 9 cups of juice, we first need to determine how many groups of 2 cups of juice are in 9 cups.
\( 9 \text{ cups of juice} \div 2 \text{ cups of juice/group} = 4.5 \text{ groups} \)
Now, we can use the relationship from our double number line to find the number of cups of strawberries needed. Since for every 2 cups of juice we need 3 cups of strawberries, we can multiply the number of groups (4.5) by the amount of strawberries needed per group (3 cups):
\[ 4.5 \text{ groups} \times 3 \text{ cups of strawberries/group} = 13.5 \text{ cups of strawberries} \]
Thus, for 9 cups of juice, you would need 13.5 cups of strawberries.
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