A recipe for stir fry calls for 6 cups of rice for every 4 cups of veggies. Suppose a restaurant is making a large batch of stir fry using 15 cups of veggies. How much rice would they need?

Question

Start by labeling the double number line with the cups of veggies and cups of rice that the recipe calls for.
Veggies (cups)
0
Rice (cups)
0

Answer 1

To solve the problem and create a double number line for the cups of veggies and cups of rice, we need to establish the relationship between the two ingredients according to the given recipe:

The ratio of rice to veggies from the recipe is:

• 6 cups of rice for every 4 cups of veggies.

We can simplify this ratio:

• The ratio of rice to veggies is 6:4, which simplifies to 3:2.

Now, we can set up our double number line by determining a consistent scale based on the recipe.

Double Number Line:

| Veggies (cups) | 0 | 4 | 8 | 12 | 16 | |----------------|---|---|---|----|----| | Rice (cups) | 0 | 6 | 12| 18 | 24 |

Finding Rice for 15 Cups of Veggies

Now, we need to find out how much rice is needed for 15 cups of veggies.

Using the ratio we established (3:2), we can set up a proportion based on the number of cups of veggies:

1. Set up the proportion using the known ratio: \[ \frac{3 \text{ cups of rice}}{2 \text{ cups of veggies}} = \frac{x \text{ cups of rice}}{15 \text{ cups of veggies}} \]

2. Cross-multiply: \[ 3 \cdot 15 = 2 \cdot x \] \[ 45 = 2x \]

3. Solve for \(x\): \[ x = \frac{45}{2} = 22.5 \]

Thus, the restaurant would need 22.5 cups of rice for 15 cups of veggies.