Question
If 2 buses needed to transport 75 students to the aquarium and 8 buses can transport 300 students, what proportion describes the relationship between the number of buses and the number of students? (Do not reduce the ratios to their lowest terms
Answers
GPT-4o mini
To find the proportion that describes the relationship between the number of buses and the number of students, we can set up a ratio based on the provided information.
From the first scenario:
- 2 buses transport 75 students.
This gives us the ratio:
\[
\text{Ratio of buses to students} = \frac{2 \text{ buses}}{75 \text{ students}}
\]
From the second scenario:
- 8 buses transport 300 students.
This gives us the ratio:
\[
\text{Ratio of buses to students} = \frac{8 \text{ buses}}{300 \text{ students}}
\]
We can express the relationship in terms of a single proportion. Both scenarios provide valid ratios describing the same relationship between the number of buses (B) and the number of students (S). Thus, we can state:
\[
\frac{B}{S} = \frac{2}{75} \quad \text{and} \quad \frac{B}{S} = \frac{8}{300}
\]
Therefore, the proportion that describes the relationship between the number of buses and the number of students can be written as:
\[
\frac{2}{75} = \frac{8}{300}
\]
This is the proportion that illustrates the relationship between the number of buses and the number of students without reducing the ratios to their lowest terms.
From the first scenario:
- 2 buses transport 75 students.
This gives us the ratio:
\[
\text{Ratio of buses to students} = \frac{2 \text{ buses}}{75 \text{ students}}
\]
From the second scenario:
- 8 buses transport 300 students.
This gives us the ratio:
\[
\text{Ratio of buses to students} = \frac{8 \text{ buses}}{300 \text{ students}}
\]
We can express the relationship in terms of a single proportion. Both scenarios provide valid ratios describing the same relationship between the number of buses (B) and the number of students (S). Thus, we can state:
\[
\frac{B}{S} = \frac{2}{75} \quad \text{and} \quad \frac{B}{S} = \frac{8}{300}
\]
Therefore, the proportion that describes the relationship between the number of buses and the number of students can be written as:
\[
\frac{2}{75} = \frac{8}{300}
\]
This is the proportion that illustrates the relationship between the number of buses and the number of students without reducing the ratios to their lowest terms.