To determine how much rice is needed for 15 cups of veggies, we can use the ratio from the recipe, which states that for every 5 cups of veggies, 6 cups of rice are required.
We can set up a proportion based on the given amounts.
If 5 cups of veggies require 6 cups of rice, we can express the relationship as:
\[ \frac{6 \text{ cups of rice}}{5 \text{ cups of veggies}} = \frac{x \text{ cups of rice}}{15 \text{ cups of veggies}} \]
To solve for \(x\), we can cross-multiply:
\[ 6 \times 15 = 5 \times x \]
Calculating the left side:
\[ 90 = 5x \]
Next, we solve for \(x\) by dividing both sides by 5:
\[ x = \frac{90}{5} = 18 \]
Thus, the restaurant would need 18 cups of rice for 15 cups of veggies.