A recipe for stir fry calls for 10 cups of rice for every 6 cups of veggies. Suppose a restaurant is making a large batch of stir fry using 9 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 create a double number line for the stir fry recipe, we'll first establish the relationship between the cups of rice and cups of veggies based on the original recipe.

The original recipe states that for every 6 cups of veggies, you need 10 cups of rice. This can be set up in a ratio:

\[ \frac{\text{rice}}{\text{veggies}} = \frac{10 \text{ cups rice}}{6 \text{ cups veggies}} = \frac{5}{3} \]

Now, we'll set up the double number line with the given ratio:

Double Number Line

Veggies (cups)
0 | 6 | 12
-------------|---------------|---------
Rice (cups)
0 | 10 | 20

We can see that if you have 0 cups of veggies, you have 0 cups of rice, and if you have 6 cups of veggies, you have 10 cups of rice. Since the recipe indicates a linear relationship, if we increase the amount of veggies, we increase the amount of rice proportionally.

To find out how much rice is needed for 9 cups of veggies, we set up a proportion based on the established ratio:

Let \(x\) be the amount of rice needed for 9 cups of veggies:

\[ \frac{x}{9} = \frac{10}{6} \]

Cross-multiply to solve for \(x\):

\[ 6x = 10 \times 9 \]

\[ 6x = 90 \]

Now, divide both sides by 6:

\[ x = \frac{90}{6} = 15 \]

So, for 9 cups of veggies, the restaurant would need 15 cups of rice.

Summary

• For 6 cups of veggies, you need 10 cups of rice.
• For 9 cups of veggies, based on the ratio, you need 15 cups of rice.