A recipe for stir fry calls for 6 cups of rice for every 5 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 solve the problem, we can set up a double number line that reflects the relationship between the cups of rice and the cups of veggies based on the original recipe.

The recipe states that for every 5 cups of veggies, 6 cups of rice are required. We can create a proportion to find out how much rice is needed for 15 cups of veggies.

Here's how to label the double number line:

1. Cups of Veggies: 0, 5, 10, 15
2. Cups of Rice: 0, 6, 12, ?

Now, we can use the ratio from the recipe to fill in the missing value for 15 cups of veggies.

Starting from the recipe ratio:

• 5 cups of veggies → 6 cups of rice

Now, if we scale that up:

• For 10 cups of veggies (which is double 5 cups), we would need double the rice:
  • \(10\) cups of veggies → \(12\) cups of rice (since \(6 \times 2 = 12\))

Now we calculate for 15 cups of veggies. The ratio of veggies to rice can be expressed as: \[ \frac{\text{Cups of rice}}{\text{Cups of veggies}} = \frac{6}{5} \] To find the rice required for 15 cups of veggies, set up the equation: \[ \frac{r}{15} = \frac{6}{5} \] Cross-multiplying gives: \[ 5r = 6 \times 15 \] Calculating the right-hand side: \[ 5r = 90 \] Now, divide both sides by 5 to solve for \(r\): \[ r = \frac{90}{5} = 18 \]

Therefore, the restaurant would need 18 cups of rice for 15 cups of veggies.

Summary

On the double number line, it would look like this:

\[ \begin{array}{|c|c|} \hline \text{Cups of Veggies} & \text{Cups of Rice} \ \hline 0 & 0 \ 5 & 6 \ 10 & 12 \ 15 & 18 \ \hline \end{array} \]

In conclusion, the restaurant needs 18 cups of rice for 15 cups of veggies.