Question
Can you think of a real world example that you need to translate word problems into simultaneous equations ( with two variables)
Answers
GPT-4o mini
Certainly! A real-world example of translating a word problem into simultaneous equations with two variables could involve a situation related to budget allocation for a school event.
### Example Scenario:
Imagine a school is planning a field trip, and they need to arrange transportation. The school has two options for buses. They can either hire a small bus or a large bus. The small bus costs $300 and can carry 20 students, while the large bus costs $500 and can carry 40 students. The school has a total budget of $2,000 and needs to transport exactly 100 students.
### Setting Up the Problem:
1. **Define the Variables:**
- Let \( x \) represent the number of small buses hired.
- Let \( y \) represent the number of large buses hired.
2. **Create the Equations:**
- The first equation represents the total number of students:
\[
20x + 40y = 100
\]
- The second equation represents the total budget:
\[
300x + 500y = 2000
\]
### Solving the System of Equations:
Now, you have a system of two simultaneous equations:
1. \( 20x + 40y = 100 \)
2. \( 300x + 500y = 2000 \)
From here, you can solve the equations simultaneously to find the number of small and large buses needed to transport all 100 students without exceeding the budget of $2,000.
This example demonstrates how real-life situations involving budget constraints and requirements can be modeled with simultaneous equations.
### Example Scenario:
Imagine a school is planning a field trip, and they need to arrange transportation. The school has two options for buses. They can either hire a small bus or a large bus. The small bus costs $300 and can carry 20 students, while the large bus costs $500 and can carry 40 students. The school has a total budget of $2,000 and needs to transport exactly 100 students.
### Setting Up the Problem:
1. **Define the Variables:**
- Let \( x \) represent the number of small buses hired.
- Let \( y \) represent the number of large buses hired.
2. **Create the Equations:**
- The first equation represents the total number of students:
\[
20x + 40y = 100
\]
- The second equation represents the total budget:
\[
300x + 500y = 2000
\]
### Solving the System of Equations:
Now, you have a system of two simultaneous equations:
1. \( 20x + 40y = 100 \)
2. \( 300x + 500y = 2000 \)
From here, you can solve the equations simultaneously to find the number of small and large buses needed to transport all 100 students without exceeding the budget of $2,000.
This example demonstrates how real-life situations involving budget constraints and requirements can be modeled with simultaneous equations.