Question

A recipe for biryani calls for 3 cups of rice for every
4
1
​
cup of chopped onions. Using the same recipe, how many cups of onions will you need for 6 cups of rice? Use the constant of proportionality to help you solve.
Start by setting up a table that could be used to find how many cups of onions you will need for 6 cups of rice.
Cups of Rice Cups of Onions

Answer 1

To determine how many cups of onions are needed for 6 cups of rice using the given recipe ratio, let's first examine the ratio provided:

The recipe states that for every 3 cups of rice, you need 4.1 cups of chopped onions. We can set up a proportional relationship between the cups of rice and the cups of onions.

### Step 1: Set up the relationship
The relationship can be expressed as:
- For 3 cups of rice, the necessary amount of chopped onions is 4.1 cups.

To find a constant of proportionality (k), we can figure out how many cups of onions correspond to one cup of rice:

#### Finding the Constant of Proportionality
\[
k = \frac{\text{cups of onions}}{\text{cups of rice}} = \frac{4.1}{3}
\]

### Step 2: Set up the table
Now, let's create a table to show the connection between the cups of rice and the cups of onions.

| Cups of Rice | Cups of Onions |
|--------------|-----------------|
| 3 | 4.1 |
| 6 | ? |

### Step 3: Solve for Cups of Onions
Now we can find out how many cups of onions are needed for 6 cups of rice using the calculated constant of proportionality (k).

Using the ratio, we have:
\[
\text{Cups of Onions} = k \times \text{Cups of Rice}
\]

For 6 cups of rice:
\[
\text{Cups of Onions} = \frac{4.1}{3} \times 6
\]
Calculating this:
\[
\text{Cups of Onions} = \frac{4.1 \times 6}{3} = \frac{24.6}{3} = 8.2
\]

### Step 4: Update the table
Now we can fill in the table with the calculated value:

| Cups of Rice | Cups of Onions |
|--------------|-----------------|
| 3 | 4.1 |
| 6 | 8.2 |

### Conclusion
You will need **8.2 cups of onions** for **6 cups of rice** based on the given recipe.