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

Answer 1

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.