Question
A Girl Scout is selling cookies to raise money for her troop. She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day. The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.
Girl Scout Cookie Fundraiser
Time (in days) 1 3 4 7
Number of Boxes 25 21 19 13
Which of the following graphs shows the relationship given in the table?
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 21
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 23 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 25 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 23
Girl Scout Cookie Fundraiser
Time (in days) 1 3 4 7
Number of Boxes 25 21 19 13
Which of the following graphs shows the relationship given in the table?
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 21
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 23 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 25 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 23
Answers
GPT-4o mini
To determine which graph accurately represents the relationship between the number of days and the number of boxes remaining based on the provided table, we can first analyze the data and identify a pattern.
The data given is:
- Day 1: 25 boxes remaining
- Day 3: 21 boxes remaining
- Day 4: 19 boxes remaining
- Day 7: 13 boxes remaining
Next, we can calculate how many boxes are sold over the spans of days:
- From Day 1 to Day 3 (2 days):
\( 25 - 21 = 4 \) boxes sold
Therefore, \( 4 \text{ boxes in } 2 \text{ days } \Rightarrow 2 \text{ boxes per day}. \)
- From Day 3 to Day 4 (1 day):
\( 21 - 19 = 2 \) boxes sold
Therefore, \( 2 \text{ boxes in } 1 \text{ day } \Rightarrow 2 \text{ boxes per day}. \)
- From Day 4 to Day 7 (3 days):
\( 19 - 13 = 6 \) boxes sold
Therefore, \( 6 \text{ boxes in } 3 \text{ days } \Rightarrow 2 \text{ boxes per day}. \)
Based on this, the Girl Scout consistently sells about 2 boxes a day.
Now, we can extrapolate to find out how many boxes she would have initially if this pattern continues. If she sells 2 boxes a day, then on Day 0 (the day before she started selling) she would likely have:
\( 25 + 2 = 27 \)
Thus, we can deduce that she started with **27 boxes on Day 0**.
The possible graphs provided include starting points, and we found a starting point of 27 boxes. Let's evaluate the options:
1. **0 comma 27 and 2 comma 21**: This implies that at Day 2 she would have 21 boxes remaining, consistent with selling 2 boxes per day.
2. **0 comma 23 and 2 comma 19**: This does not line up with our findings.
3. **0 comma 25 and 2 comma 19**: This does not line up with our findings.
4. **0 comma 27 and 2 comma 23**: This would imply selling only 2 boxes to reach 23, which is consistent with one selling day but not with the overall data.
By analyzing the options' coordinates against our calculations, the first option, which passes through the points (0, 27) and (2, 21), accurately reflects the initial boxes sold and aligns with the decrease noted day by day in the data.
Thus, the correct answer is:
**a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 21.**
The data given is:
- Day 1: 25 boxes remaining
- Day 3: 21 boxes remaining
- Day 4: 19 boxes remaining
- Day 7: 13 boxes remaining
Next, we can calculate how many boxes are sold over the spans of days:
- From Day 1 to Day 3 (2 days):
\( 25 - 21 = 4 \) boxes sold
Therefore, \( 4 \text{ boxes in } 2 \text{ days } \Rightarrow 2 \text{ boxes per day}. \)
- From Day 3 to Day 4 (1 day):
\( 21 - 19 = 2 \) boxes sold
Therefore, \( 2 \text{ boxes in } 1 \text{ day } \Rightarrow 2 \text{ boxes per day}. \)
- From Day 4 to Day 7 (3 days):
\( 19 - 13 = 6 \) boxes sold
Therefore, \( 6 \text{ boxes in } 3 \text{ days } \Rightarrow 2 \text{ boxes per day}. \)
Based on this, the Girl Scout consistently sells about 2 boxes a day.
Now, we can extrapolate to find out how many boxes she would have initially if this pattern continues. If she sells 2 boxes a day, then on Day 0 (the day before she started selling) she would likely have:
\( 25 + 2 = 27 \)
Thus, we can deduce that she started with **27 boxes on Day 0**.
The possible graphs provided include starting points, and we found a starting point of 27 boxes. Let's evaluate the options:
1. **0 comma 27 and 2 comma 21**: This implies that at Day 2 she would have 21 boxes remaining, consistent with selling 2 boxes per day.
2. **0 comma 23 and 2 comma 19**: This does not line up with our findings.
3. **0 comma 25 and 2 comma 19**: This does not line up with our findings.
4. **0 comma 27 and 2 comma 23**: This would imply selling only 2 boxes to reach 23, which is consistent with one selling day but not with the overall data.
By analyzing the options' coordinates against our calculations, the first option, which passes through the points (0, 27) and (2, 21), accurately reflects the initial boxes sold and aligns with the decrease noted day by day in the data.
Thus, the correct answer is:
**a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 21.**