A recipe for mac and cheese calls for 6 cups of pasta for every 4 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 set up a double number line for the recipe, we need to understand the ratio between cups of pasta and cups of cheese. According to the recipe, 6 cups of pasta goes with 4 cups of cheese.

Double Number Line:

| Cups of Cheese | Cups of Pasta | |----------------|----------------| | 0 | 0 | | 4 | 6 | | 8 | 12 | | 12 | 18 | | 16 | 24 |

Now, using the ratio of 6 cups of pasta for every 4 cups of cheese, we can find out how much pasta is needed for 15 cups of cheese.

1. Calculate the ratio conversion: The ratio of pasta to cheese is 6:4, which can be simplified to 3:2.

2. Set up the proportion: Let \( x \) be the number of cups of pasta needed for 15 cups of cheese:

   \[ \frac{3 \text{ cups of pasta}}{2 \text{ cups of cheese}} = \frac{x}{15 \text{ cups of cheese}} \]

3. Cross multiply to solve for \( x \):

   \[ 3 \cdot 15 = 2 \cdot x \]

   \[ 45 = 2x \]

   \[ x = \frac{45}{2} = 22.5 \]

Thus, the restaurant would need 22.5 cups of pasta to go with 15 cups of cheese for their mac and cheese.