Question

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?
Now, use the double number line to find the number of cups of strawberries you would need for 9 cups of juice.
Juice (cups)
0
1
2
9
Strawberries (cups)
0
1
2
1
​

3

Answer 1

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**.