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
5
Pasta (cups)
0
6
Great job!
To find how many cups of pasta they’d need for 15 cups of cheese, it can be helpful to first find the unit rate, or the amount of pasta needed for 1 cup of cheese. Partition the number line to find the number of cups of pasta needed for every 1 cup of cheese.
Cheese (cups)
0
5
Pasta (cups)
0
6

Answer 1

To find the unit rate of pasta needed for each cup of cheese, we start with the original ratio given in the recipe. The recipe states that for every 5 cups of cheese, you need 6 cups of pasta.

Step 1: Find the unit rate (pasta per cup of cheese)

To find how many cups of pasta are needed for 1 cup of cheese, we can divide the number of cups of pasta by the number of cups of cheese:

\[ \text{Pasta per cup of cheese} = \frac{6 \text{ cups of pasta}}{5 \text{ cups of cheese}} = \frac{6}{5} \text{ cups of pasta per cup of cheese} \]

Step 2: Set up a double number line

Now, we can label the double number line with the unit rate:

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

Step 3: Find the amount of pasta needed for 15 cups of cheese

Now that we know the ratio of pasta to cheese, we can calculate how much pasta is needed for 15 cups of cheese. We can use the unit rate:

\[ \text{Pasta needed for 15 cups of cheese} = 15 \text{ cups of cheese} \times \frac{6 \text{ cups of pasta}}{5 \text{ cups of cheese}} \]

\[ \text{Pasta needed} = 15 \times \frac{6}{5} \] \[ \text{Pasta needed} = 15 \times 1.2 = 18 \text{ cups of pasta} \]

Final Answer:

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