To determine which graph correctly represents the number of boxes of cookies the scout has over time, we need to analyze the problem statement carefully.
The scout starts with 100 boxes of cookies and sells 25 boxes every 3 hours. This means:
- At time \( t = 0 \) hours, they have 100 boxes.
- After 3 hours, they sell 25 boxes, so they'll have \( 100 - 25 = 75 \) boxes.
- After 6 hours, they sell another 25 boxes, so they'll have \( 75 - 25 = 50 \) boxes.
- After 9 hours, they sell another 25 boxes, so they'll have \( 50 - 25 = 25 \) boxes.
- After 12 hours, they’ll sell another 25 boxes (if they had any left), leading to 0 boxes.
So, the following points can be plotted based on this information:
- At \( t = 0 \): 100 boxes
- At \( t = 3 \): 75 boxes
- At \( t = 6 \): 50 boxes
- At \( t = 9 \): 25 boxes
Now we need to see which graph shows this relationship:
- The first graph shows points at: (0, 100), (1, 200), (2, 300), (3, 400), which do not match.
- The second graph shows points at: (0, 100), (3, 75), (6, 50), (9, 25), which matches perfectly.
- The third graph has incremental points decreasing by 1 every hour, which does not match.
- The fourth graph shows points at: (0, 100), (3, 125), (6, 150), (9, 175), which does not match.
Therefore, the correct graph is the second one:
- Points: (0, 100), (3, 75), (6, 50), (9, 25).