Simpler Version:

Problem: Planning a School Trip Budget

You are a member of the student council at your school, and you have been assigned the task of planning a school trip for your Year 9 class. Your goal is to create a budget for the trip that ensures all expenses are covered while keeping the cost per student as low as possible.

Here are the details of the trip:

- Destination: A local museum

- Number of students: 30

- Number of teachers: 3

- Cost per student: $20 (includes transportation, museum entry, and lunch)

- Cost per teacher: $0 (teachers' expenses are covered separately)

Your task is to determine the total cost of the trip and calculate the amount each student needs to contribute to cover the expenses.

1. Calculate the total cost of the trip:

- Multiply the number of students by the cost per student.

- Add any additional expenses, such as transportation costs or museum entry fees.

2. Determine the amount each student needs to contribute:

- Divide the total cost of the trip by the number of students.

- Round the amount to the nearest dollar to ensure a whole number.

3. Create a linear equation to represent the situation:

- Let "x" represent the amount each student needs to contribute.

- Write an equation that represents the total cost of the trip in terms of "x" and solve for "x".

Real-world application:

This problem-solving task simulates a real-world scenario where students need to plan and budget for a school trip. By incorporating linear equations, students can practice their algebraic skills while also developing critical thinking and problem-solving abilities. This simplified version allows students to focus on the basic concepts of budgeting and cost division.

Same Version:

Problem: Planning a School Trip Budget

You are a member of the student council at your school, and you have been assigned the task of planning a school trip for your Year 9 class. Your goal is to create a budget for the trip that ensures all expenses are covered while keeping the cost per student as low as possible.

Here are the details of the trip:

- Destination: A local zoo

- Number of students: 40

- Number of teachers: 4

- Cost per student: $25 (includes transportation, zoo entry, and lunch)

- Cost per teacher: $0 (teachers' expenses are covered separately)

Your task is to determine the total cost of the trip and calculate the amount each student needs to contribute to cover the expenses.

1. Calculate the total cost of the trip:

- Multiply the number of students by the cost per student.

- Add any additional expenses, such as transportation costs or zoo entry fees.

2. Determine the amount each student needs to contribute:

- Divide the total cost of the trip by the number of students.

- Round the amount to the nearest dollar to ensure a whole number.

3. Create a linear equation to represent the situation:

- Let "x" represent the amount each student needs to contribute.

- Write an equation that represents the total cost of the trip in terms of "x" and solve for "x".

Real-world application:

This problem-solving task simulates a real-world scenario where students need to plan and budget for a school trip. By incorporating linear equations, students can practice their algebraic skills while also developing critical thinking and problem-solving abilities. This version maintains the same level of complexity as the original, allowing students to apply their knowledge to a different scenario.

More Complex Version:

Problem: Planning a School Trip Budget

You are a member of the student council at your school, and you have been assigned the task of planning a school trip for your Year 9 class. Your goal is to create a budget for the trip that ensures all expenses are covered while keeping the cost per student as low as possible.

Here are the details of the trip:

- Destination: A theme park in a neighboring city

- Number of students: 60

- Number of teachers: 6

- Cost per student: $40 (includes transportation, park entry, lunch, and snacks)

- Cost per teacher: $20 (includes transportation, park entry, lunch, and snacks)

Your task is to determine the total cost of the trip and calculate the amount each student needs to contribute to cover the expenses.

1. Calculate the total cost of the trip:

- Multiply the number of students by the cost per student.

- Multiply the number of teachers by the cost per teacher.

- Add any additional expenses, such as transportation costs or park entry fees.

2. Determine the amount each student needs to contribute:

- Divide the total cost of the trip by the number of students.

- Round the amount to the nearest dollar to ensure a whole number.

3. Create a linear equation to represent the situation:

- Let "x" represent the amount each student needs to contribute.

- Write an equation that represents the total cost of the trip in terms of "x" and solve for "x".

Real-world application:

This problem-solving task simulates a real-world scenario where students need to plan and budget for a school trip. By incorporating linear equations, students can practice their algebraic skills while also developing critical thinking and problem-solving abilities. This more complex version introduces additional expenses for teachers and a larger group size, challenging students to apply their knowledge to a more intricate situation.