To analyze the sales of cookies by Peter and Catherine, let's start by calculating the remaining boxes of cookies for Peter after a certain number of days, and then we can compare it to Catherine's sales.
Peter's Sales
- Initial Boxes: 300
- Sales Rate: 15 boxes per day
The number of boxes Peter has left after \( x \) days can be represented by the equation: \[ \text{Boxes left} = 300 - 15x \]
Catherine's Sales
From the table, we have the following information regarding Catherine's boxes of cookies left after \( x \) days:
| \( x \) (Days) | \( y \) (Boxes left) | |----------------|-----------------------| | 0 | 300 | | 1 | 250 | | 2 | 200 | | 3 | 150 |
Analyzing Catherine's Sales
To find the selling rate for Catherine, we can observe the changes in boxes over the days:
- From Day 0 to Day 1: \( 300 - 250 = 50 \) boxes sold
- From Day 1 to Day 2: \( 250 - 200 = 50 \) boxes sold
- From Day 2 to Day 3: \( 200 - 150 = 50 \) boxes sold
So, Catherine sells 50 boxes of cookies per day.
Comparing Peter and Catherine's Sales
Now, we can create a table for Peter's remaining boxes after the same number of days:
| \( x \) (Days) | Peter's boxes left | Catherine's boxes left | |----------------|---------------------|-----------------------| | 0 | \( 300 - 15(0) = 300 \) | 300 | | 1 | \( 300 - 15(1) = 285 \) | 250 | | 2 | \( 300 - 15(2) = 270 \) | 200 | | 3 | \( 300 - 15(3) = 255 \) | 150 |
Summary
- Peter starts with 300 boxes and sells 15 boxes a day.
- Catherine starts with 300 boxes and sells 50 boxes a day.
After three days, Peter will have 255 boxes left, while Catherine will have 150 boxes left. This means Catherine is selling her cookies at a faster rate than Peter, and her inventory is depleting much quicker.