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.
Cheese (cups)
0
4
Pasta (cups)
0
6
You got it!
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
4
Pasta (cups)
0
6
Excellent!
Label the bottom number line to find the number of cups of pasta the restaurant would need for 1 cup of cheese.
Cheese (cups)
0
1
2
3
4
Pasta (cups)
0
6

Answer 1

To determine how much pasta the restaurant would need for 15 cups of cheese, we can first find the unit rate of pasta per cup of cheese based on the original recipe:

1. According to the recipe, 4 cups of cheese corresponds to 6 cups of pasta.

   To find the pasta needed for 1 cup of cheese: \[ \text{Pasta per cup of cheese} = \frac{6 \text{ cups of pasta}}{4 \text{ cups of cheese}} = 1.5 \text{ cups of pasta per cup of cheese} \]

Now we can label the bottom number line based on this unit rate:

• Cheese (cups):
  0, 1, 2, 3, 4
• Pasta (cups):
  0, 1.5, 3, 4.5, 6

Next, we can use this unit rate to calculate the amount of pasta needed for 15 cups of cheese.

2. To find the total cups of pasta needed for 15 cups of cheese: \[ \text{Total pasta} = 1.5 \text{ cups of pasta per cup of cheese} \times 15 \text{ cups of cheese} = 22.5 \text{ cups of pasta} \]

Therefore, the restaurant would need 22.5 cups of pasta for 15 cups of cheese.