Question

A group of friends wants to go to the amusement park. They have $214.50 to spend on parking and admission. Parking is $12, and tickets cost $33.75 per person, including tax. Which tape diagram could be used to represent the context if pp represents the number of people who can go to the amusement park?

Answer 1

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:

1. **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:
\[
\text{Total cost} = 12 + 33.75 \times pp
\]

2. **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).

3. **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 \( pp \).