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.
Veggies (cups)
0
6
Rice (cups)
0
8
Great job!
To find how many cups of rice they’d need for 15 cups of veggies, it can be helpful to first find the unit rate, or the amount of rice needed for 1 cup of veggies. Partition the number line to find the number of cups of rice needed for every 1 cup of veggies.

Answer 1

To find the unit rate (the amount of rice needed for 1 cup of veggies), we can start with the proportions given in the recipe:

The recipe ratio for rice to veggies is:

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

To find the amount of rice needed for 1 cup of veggies, we can divide both the cups of rice and the cups of veggies by 6:

\[ \text{Rice per cup of veggies} = \frac{8 \text{ cups of rice}}{6 \text{ cups of veggies}} = \frac{4}{3} \text{ cups of rice per cup of veggies}. \]

Now, we can use this unit rate to find out the amount of rice needed for 15 cups of veggies:

\[ \text{Rice for 15 cups of veggies} = 15 \text{ cups of veggies} \times \frac{4}{3} \text{ cups of rice per cup of veggies}. \]

Calculating that gives:

\[ 15 \times \frac{4}{3} = 15 \times 1.33\overline{3} = 20 \text{ cups of rice}. \]

So, the restaurant would need 20 cups of rice for 15 cups of veggies.