A recipe for mac and cheese calls for 6 cups of pasta for every 5 cups of cheese. Suppose a restaurant is making a large batch of mac and cheese using 15 cups of cheese. How much pasta would they need?

Question

Start by labeling the double number line with the cups of cheese and cups of pasta that the recipe calls for.

Answer 1

To create a double number line for the mac and cheese recipe, we need to set up the relationship between the cups of cheese and cups of pasta according to the recipe's proportions.

From the recipe, we know:

• For every 5 cups of cheese, we use 6 cups of pasta.

Let's set up the double number line based on that proportion:

Cups of Cheese:       0          5            10           15
Cups of Pasta:        0          6            12           18

Now, using the information that the restaurant is using 15 cups of cheese, we can find the corresponding amount of pasta.

1. Identify the ratio from the double number line:

   • For 5 cups of cheese, we need 6 cups of pasta.
   • Therefore, for 10 cups of cheese (which is double 5 cups), we would need double the pasta, which is 12 cups of pasta.
   • For 15 cups of cheese (which is 3 times 5 cups), we would need to calculate the pasta as follows:

2. Calculate the required pasta:

   • The ratio of cheese to pasta is: \[ \text{Pasta} = \frac{6 \text{ cups of pasta}}{5 \text{ cups of cheese}} \times \text{Cups of cheese} \]
   • Substituting the value for cheese: \[ \text{Pasta} = \frac{6}{5} \times 15 = 18 \text{ cups of pasta} \]

So, for 15 cups of cheese, the restaurant would need 18 cups of pasta.