High School

Model Real Life:

You are testing how many grams different-sized bundles of spaghetti can hold. You predict that a bundle of 5 noodles can hold 10 quarters before breaking and that a bundle of 10 noodles can hold 20 quarters before breaking. Each quarter weighs 5 grams.

Using your predictions, how many more grams can the bundle of 10 noodles hold than the bundle of 5 noodles?

Answer :

Final answer:

The bundle of 10 noodles can hold 50 grams more than the bundle of 5 noodles, as it can support 100 grams while the 5-noodle bundle can support only 50 grams.

Explanation:

To determine how many more grams the bundle of 10 noodles can hold compared to the bundle of 5 noodles, we first calculate the weight each bundle can support and then find the difference. According to the prediction, a bundle of 5 noodles can hold 10 quarters, and each quarter weighs 5 grams.

Weight supported by 5 noodles = 10 quarters × 5 grams/quarter = 50 grams.

Weight supported by 10 noodles = 20 quarters × 5 grams/quarter = 100 grams.

The difference in capacity between the bundles is therefore:

Difference in capacity = Weight supported by 10 noodles - Weight supported by 5 noodles.

Difference in capacity = 100 grams - 50 grams = 50 grams.

The bundle of 10 noodles can hold 50 grams more than the bundle of 5 noodles.

To solve this problem, we first need to calculate the weight that each bundle of spaghetti noodles can hold according to your predictions, and then determine the difference in weight between the two bundles.

1. First, we calculate the weight each bundle can hold in grams.

- Each quarter weighs 5 grams.

- A bundle of 5 noodles can hold 10 quarters.

- A bundle of 10 noodles can hold 20 quarters.

2. Next, we calculate the total weight each bundle can hold.

- Weight held by 5 noodles = 10 quarters × 5 grams/quarter

- Weight held by 10 noodles = 20 quarters × 5 grams/quarter

3. Finally, we find the difference in weight between the two bundles.

Let's calculate these:

According to the calculations:

- A bundle of 5 noodles can hold 50 grams (10 quarters × 5 grams/quarter).

- A bundle of 10 noodles can hold 100 grams (20 quarters × 5 grams/quarter).

The difference in weight that the bundle of 10 noodles can hold compared to the bundle of 5 noodles is 50 grams.