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
1.5
6
Excellent!
The recipe calls for 1
2
1
​
cups of pasta for every 1 cup of cheese. Now, use the double number line to find the number of cups of pasta the restaurant would need for 15 cups of cheese. Solve on paper, then enter your answer on Zearn.
Cheese (cups)
0
1
2
3
4
15
Pasta (cups)
0
1
2
1
​

6

Answer 1

To find out how many cups of pasta the restaurant needs for 15 cups of cheese, we first found that the recipe requires 1.5 cups of pasta for each cup of cheese.

We can use this unit rate to determine the amount of pasta needed for 15 cups of cheese:

1. Calculate the amount of pasta needed: Multiply the number of cups of cheese (15 cups) by the amount of pasta needed per cup of cheese (1.5 cups).

   \[ \text{Pasta needed} = \text{Cups of cheese} \times \text{Pasta per cup of cheese} \]

   \[ \text{Pasta needed} = 15 \times 1.5 \]

   \[ \text{Pasta needed} = 22.5 \]

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