To represent the situation with a tape diagram, we need to break down the total expenses, which include parking and admission tickets based on the number of people attending.
Given:
- Total budget: $214.50
- Parking cost: $12
- Admission ticket cost per person: $33.75
- Let \( pp \) represent the number of people.
Steps to Set Up the Tape Diagram:
-
Total Expenses: The total expenses consist of the parking cost plus the total cost of admission for all the people: \[ \text{Total cost} = \text{Parking} + \text{Admission for } pp \text{ people} \] This can be expressed as: \[ \text{Total cost} = 12 + 33.75 \times pp \]
-
Budget Constraint: The total cost must not exceed the budget: \[ 12 + 33.75 \times pp \leq 214.50 \]
Tape Diagram Representation:
In the tape diagram, you can use the following representation:
- One section for Parking: A segment labeled "Parking ($12)"
- Multiple sections for Admission: A longer segment that is divided into \( pp \) equal parts, where each part is labeled $33.75 (Admission ticket for 1 person).
- Connecting the Total: The entire length of the tape would represent the total budget of $214.50 with a visual representation showing:
- One segment of length representing $12 for parking.
- \( pp \) segments of length $33.75 each for the admission costs.
In summary, a tape diagram could be structured as follows:
- Total tape length representing $214.50
- One segment (short) for Parking ($12)
- \( pp \) segments (each of equal length) for Admission ($33.75 per person)
This visual will clearly show how the budget is allocated for parking and admission based on the number of people \( pp \).
5 answers