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
Nice!
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.

Answer 1

To find the amount of pasta needed for every 1 cup of cheese, we start with the original ratio given in the recipe, which is 6 cups of pasta for every 5 cups of cheese.

1. Find the unit rate of pasta per cup of cheese: \[ \text{Unit rate} = \frac{\text{Cups of pasta}}{\text{Cups of cheese}} = \frac{6 \text{ cups pasta}}{5 \text{ cups cheese}} = 1.2 \text{ cups pasta per cup cheese} \]

2. Now that we have the unit rate, we can calculate the amount of pasta needed for 15 cups of cheese: \[ \text{Amount of pasta} = \text{Cups of cheese} \times \text{Unit rate} \] \[ \text{Amount of pasta} = 15 \text{ cups cheese} \times 1.2 \text{ cups pasta per cup cheese} = 18 \text{ cups pasta} \]

So, the restaurant would need 18 cups of pasta for 15 cups of cheese.

Summary of the double number line:

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

This shows that for every 5 cups of cheese, 6 cups of pasta are required, and for 15 cups of cheese, 18 cups of pasta is needed.