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.
Cheese (cups)
0
Pasta (cups)
0

Answer 1

To find out how much pasta is needed for 15 cups of cheese based on the given recipe ratio of pasta to cheese (6 cups of pasta for every 5 cups of cheese), you can set up a double number line.

Step 1: Establish the Ratio

From the recipe:

• 6 cups of pasta for 5 cups of cheese

This translates to the ratio: \[ \frac{Pasta}{Cheese} = \frac{6}{5} \]

Step 2: Set Up the Double Number Line

Now we'll create the double number line with the known values:

Cheese (cups)      |   0   |  5   |  10  |  15  | 
Pasta (cups)      |   0   |  6   |  12  |  18  | 

Step 3: Calculate the Pasta for 15 Cups of Cheese

To find how much pasta corresponds to 15 cups of cheese, we can use the ratio:

Using the ratio \( \frac{\text{Pasta}}{\text{Cheese}} = \frac{6}{5} \):

We want to find the amount of pasta (\(x\)) that corresponds to 15 cups of cheese: \[ \frac{x}{15} = \frac{6}{5} \]

Step 4: Solve the Equation

Cross-multiplying gives us: \[ 5x = 6 \times 15 \] \[ 5x = 90 \] \[ x = \frac{90}{5} \] \[ x = 18 \]

Conclusion

The restaurant would need 18 cups of pasta for 15 cups of cheese.

Here’s the summary filled into the double number line:

Cheese (cups)       |   0   |  5   |  10  |  15  | 
Pasta (cups)       |   0   |  6   |  12  |  18  | 

Therefore, for 15 cups of cheese, you need 18 cups of pasta.