A recipe for stir fry calls for 8 cups of rice for every 6 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.

Answer 1

To set up the double number line for the stir fry recipe, we can start with the ratio given in the recipe:

• The recipe calls for 8 cups of rice for every 6 cups of veggies.

Now, let's establish our double number line with the two quantities.

Cups of Veggies: 0 6 12
Cups of Rice: 0 8 16

The increments in the cups of veggies are by 6 cups, and for every 6 cups of veggies, the corresponding cups of rice are 8 cups. As we can see, if you double the amount of veggies (12 cups), the rice will also double, resulting in 16 cups of rice.

Now that we have our double number line, let's calculate how much rice is needed for 15 cups of veggies.

Using the ratio from the recipe:

\[ \text{Rice} = \text{Veggies} \times \frac{8 \text{ cups of rice}}{6 \text{ cups of veggies}} \]

Substituting in 15 cups of veggies:

\[ \text{Rice} = 15 \times \frac{8}{6} \]

Simplifying \( \frac{8}{6} \) gives us \( \frac{4}{3} \):

\[ \text{Rice} = 15 \times \frac{4}{3} = 15 \div 3 \times 4 = 5 \times 4 = 20 \]

Therefore, the restaurant would need 20 cups of rice to go with 15 cups of veggies.