Question
a scout has 100 boxes of cookies to sell. they sell 25 boxes every 3 hours. select the graph that shows how many boxes of cookies the scout has over time.
1. <img alt="A coordinate graph shows the x-axis labeled as hours ranging from 0 to 8 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 10 in 1 unit increments. Six unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 7 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 5 comma 5 right parenthesis. A solid arrow passes through these points.
2. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 1,000 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 1 comma 200 right parenthesis, left parenthesis 2 comma 300 right parenthesis, and left parenthesis 3 comma 400 right parenthesis. A solid arrow passes through these points.
3. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 9 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 150 in increments of 25. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 3 comma 75 right parenthesis, left parenthesis 6 comma 50 right parenthesis, and left parenthesis 9 comma 25 right parenthesis. A solid arrow passes through these points.
4. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 9 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 175 in increments of 25. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 3 comma 125 right parenthesis, left parenthesis 6 comma 150 right parenthesis, and left parenthesis 9 comma 175 right parenthesis. A solid arrow passes through these points.
1. <img alt="A coordinate graph shows the x-axis labeled as hours ranging from 0 to 8 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 10 in 1 unit increments. Six unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 7 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 5 comma 5 right parenthesis. A solid arrow passes through these points.
2. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 1,000 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 1 comma 200 right parenthesis, left parenthesis 2 comma 300 right parenthesis, and left parenthesis 3 comma 400 right parenthesis. A solid arrow passes through these points.
3. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 9 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 150 in increments of 25. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 3 comma 75 right parenthesis, left parenthesis 6 comma 50 right parenthesis, and left parenthesis 9 comma 25 right parenthesis. A solid arrow passes through these points.
4. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 9 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 175 in increments of 25. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 3 comma 125 right parenthesis, left parenthesis 6 comma 150 right parenthesis, and left parenthesis 9 comma 175 right parenthesis. A solid arrow passes through these points.
Answers
GPT-4o mini
To determine which graph accurately represents the number of boxes of cookies the scout has over time, we need to analyze the selling rate and the duration.
The scout starts with 100 boxes of cookies and sells 25 boxes every 3 hours. This means:
- After 3 hours: 100 - 25 = 75 boxes left.
- After 6 hours: 100 - 50 = 50 boxes left.
- After 9 hours: 100 - 75 = 25 boxes left.
- After 12 hours: 100 - 100 = 0 boxes left.
Now let's evaluate each option to see which one matches these values:
1. **Option 1**: This graph shows a decrease from 10 boxes to 5 boxes over 5 hours. It does not correspond to the problem.
2. **Option 2**: This graph shows an increase from 100 boxes to 400 boxes over 3 hours. It also does not relate to the problem.
3. **Option 3**: This graph starts at 100 boxes (0 hours), drops to 75 boxes after 3 hours, to 50 boxes after 6 hours, and to 25 boxes after 9 hours. This matches our calculations perfectly.
4. **Option 4**: This graph inaccurately represents increasing values and does not match the selling scenario described.
Thus, the correct graph that shows how many boxes of cookies the scout has over time is **Option 3**.
The scout starts with 100 boxes of cookies and sells 25 boxes every 3 hours. This means:
- After 3 hours: 100 - 25 = 75 boxes left.
- After 6 hours: 100 - 50 = 50 boxes left.
- After 9 hours: 100 - 75 = 25 boxes left.
- After 12 hours: 100 - 100 = 0 boxes left.
Now let's evaluate each option to see which one matches these values:
1. **Option 1**: This graph shows a decrease from 10 boxes to 5 boxes over 5 hours. It does not correspond to the problem.
2. **Option 2**: This graph shows an increase from 100 boxes to 400 boxes over 3 hours. It also does not relate to the problem.
3. **Option 3**: This graph starts at 100 boxes (0 hours), drops to 75 boxes after 3 hours, to 50 boxes after 6 hours, and to 25 boxes after 9 hours. This matches our calculations perfectly.
4. **Option 4**: This graph inaccurately represents increasing values and does not match the selling scenario described.
Thus, the correct graph that shows how many boxes of cookies the scout has over time is **Option 3**.