Question

Razi’s Party Favor Bag Progress

A 2-column table with 5 rows. Column 1 is labeled Time (minutes), x with entries 0, 1, 2, 3, 4. Column 2 is labeled Bags Remaining, y with entries 52, 48, 44, 40, 36.

Seung and Razi are both filling party favor bags for their birthdays at a constant rate. Razi’s progress is shown in the table.

After 3 minutes Seung had 34 bags remaining to be filled, and after 4 minutes he had 31 bags remaining.

Compare Seung and Razi’s bag-filling progress.

Each minute Seung fills
than Razi.

Answer 1

To compare Razi and Seung's bag-filling progress, we first need to determine the rate at which both are filling the bags.

**Razi's Progress:**
From the table, we can see how many bags Razi has remaining at different times:

- At 0 minutes: 52 bags
- At 1 minute: 48 bags
- At 2 minutes: 44 bags
- At 3 minutes: 40 bags
- At 4 minutes: 36 bags

To find Razi's rate of filling bags, we can calculate the difference in the number of bags over the time periods. Razi fills:

- Between 0 and 1 minute: 52 - 48 = 4 bags
- Between 1 and 2 minutes: 48 - 44 = 4 bags
- Between 2 and 3 minutes: 44 - 40 = 4 bags
- Between 3 and 4 minutes: 40 - 36 = 4 bags

So, Razi fills bags at a constant rate of 4 bags per minute.

**Seung's Progress:**
Now let's analyze Seung's progress.

- After 3 minutes: 34 bags remaining
- After 4 minutes: 31 bags remaining

To find Seung's rate, we also calculate the difference between the number of bags he has remaining:

- Between 3 and 4 minutes: 34 - 31 = 3 bags

Therefore, Seung fills bags at a constant rate of 3 bags per minute.

**Comparison:**
Razi fills bags at a rate of 4 bags per minute, while Seung fills bags at a rate of 3 bags per minute.

Thus, we conclude that:

Each minute Seung fills **1 bag fewer** than Razi.