A recipe for mac and cheese calls for 7 cups of pasta for every 4 cups of cheese. Suppose a restaurant is making a large batch of mac and cheese using 20 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 determine how much pasta is needed for 20 cups of cheese based on the recipe that calls for 7 cups of pasta for every 4 cups of cheese, we can set up a proportion using a double number line.

Here's the information from the recipe:

• Cups of cheese: 4
• Cups of pasta: 7

Now, we can use this ratio to set up our double number line:

Cups of Cheese:    0       4       8       12      16      20     
Cups of Pasta:     0       7      14      21      28      ?

We know the ratios:

• 4 cups of cheese corresponds to 7 cups of pasta.

To find out how many cups of pasta correspond to 20 cups of cheese, we can set up the ratio:

\[ \frac{7 , \text{cups of pasta}}{4 , \text{cups of cheese}} = \frac{x , \text{cups of pasta}}{20 , \text{cups of cheese}} \]

Cross-multiplying gives us:

\[ 7 \cdot 20 = 4 \cdot x \]

Calculating the left side:

\[ 140 = 4x \]

Now, divide both sides by 4 to solve for \( x \):

\[ x = \frac{140}{4} = 35 \]

So, the restaurant would need 35 cups of pasta to go with 20 cups of cheese.

Here's the updated double number line with the information filled in:

Cups of Cheese:    0       4       8       12      16      20     
Cups of Pasta:     0       7      14      21      28      35

Final result: 35 cups of pasta are required for 20 cups of cheese.