The Key Club at Liberty Ranch High School is organizing a toilet paper drive. If each box can hold 52 rolls of toilet paper, draw a step function graph relating the number of toile... The Key Club at Liberty Ranch High School is organizing a toilet paper drive. If each box can hold 52 rolls of toilet paper, draw a step function graph relating the number of toilet paper rolls collected to the number of boxes needed for up to 350 rolls. Clearly label your graph.
Understand the Problem
The question is asking for a step function graph that shows the relationship between the number of toilet paper rolls collected and the number of boxes needed, with each box holding 52 rolls, for a range up to 350 rolls.
Answer
The step function relates rolls to boxes through intervals based on $52$ rolls per box, visualizing the number of boxes needed as the count of rolls increases.
Answer for screen readers
The step function graph will show that for every 52 rolls of toilet paper, one additional box is needed.
The points for the graph include:
- (0, 0)
- (52, 1)
- (104, 2)
- (156, 3)
- (208, 4)
- (260, 5)
- (312, 6)
- (350, 7)
Steps to Solve
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Determine Box Capacity Each box holds 52 rolls of toilet paper. Thus, the number of boxes needed can be calculated as: $$ \text{Number of boxes} = \frac{\text{Number of rolls}}{52} $$
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Identify Roll Ranges We need to calculate the number of boxes for toilet paper rolls ranging from 0 to 350 rolls. Create intervals based on multiples of 52 (i.e., from 0 to 52, 53 to 104, etc.).
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Calculate Boxes for Each Interval For each interval, calculate the number of boxes needed:
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For 0 to 52 rolls: $$ \text{Boxes} = \lceil \frac{0}{52} \rceil = 0 $$ $$ \text{Boxes} = \lceil \frac{52}{52} \rceil = 1 $$
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For 53 to 104 rolls: $$ \text{Boxes} = \lceil \frac{53}{52} \rceil = 2 $$ $$ \text{Boxes} = \lceil \frac{104}{52} \rceil = 2 $$
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Continue similarly until 350 rolls.
- Create Step Function Data Points Compile the data points derived from calculations:
- (0, 0)
- (52, 1)
- (104, 2)
- (156, 3)
- (208, 4)
- (260, 5)
- (312, 6)
- (350, 7)
- Plot the Step Function Using the data points, plot the step function on a graph, ensuring that:
- The x-axis represents the number of rolls (0 to 350).
- The y-axis represents the number of boxes.
- Clearly label axes and data points.
The step function graph will show that for every 52 rolls of toilet paper, one additional box is needed.
The points for the graph include:
- (0, 0)
- (52, 1)
- (104, 2)
- (156, 3)
- (208, 4)
- (260, 5)
- (312, 6)
- (350, 7)
More Information
This graph is a visual representation of how many boxes are required as toilet paper rolls are collected. Each step in the graph reflects the addition of another box as the number of rolls exceeds a multiple of 52.
Tips
- Forgetting to round up when calculating the number of boxes needed for rolls greater than a multiple of 52.
- Not correctly plotting data points on the graph based on the calculated intervals.
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