To determine the initial number of party favor bags Razi had to fill, we can analyze the pattern in the data provided.
From the table:
\[ \begin{array}{|c|c|} \hline \text{Time (minutes), x} & \text{Bags Remaining, y} \ \hline 4 & 36 \ 5 & 32 \ 6 & 28 \ 7 & 24 \ \hline \end{array} \]
We can observe that for every minute that passes, the bags remaining decrease by 4:
- From 4 minutes to 5 minutes: 36 - 32 = 4
- From 5 minutes to 6 minutes: 32 - 28 = 4
- From 6 minutes to 7 minutes: 28 - 24 = 4
This indicates that Razi is filling bags at a rate of 4 bags per minute.
Next, we can use the information at any time to find the initial number of bags. Let's take the first row (4 minutes):
If there are 36 bags remaining after 4 minutes, we can calculate how many bags were filled in those 4 minutes:
\[ \text{Bags Filled in 4 minutes} = 4 \text{ bags/minute} \times 4 \text{ minutes} = 16 \text{ bags} \]
So, to find the total initial number of bags, we add the bags filled and the bags remaining at the 4-minute mark:
\[ \text{Initial Number of Bags} = \text{Bags Remaining} + \text{Bags Filled in 4 minutes} = 36 + 16 = 52 \]
Thus, the initial number of party favor bags Razi had to fill is 52.
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