Question

If 2 buses are needed to transport 75 students to the aquarium and 8 buses can transport 300 students to the aquarium, which proportion describes the relationship between the number of buses and the number of students? (Do not reduce the ratios to their lowest terms.) Responses 2/75 ≠ 8/300 - no response given 75/2 = 8/300 - no response given 2/75 = 300/8 - no response given 2/75 = 8/300

Answer 1

To describe the relationship between the number of buses and the number of students, we can find the ratio of buses to students in both scenarios:

1. For 2 buses and 75 students, the ratio is:

\[ \frac{2}{75} \]

2. For 8 buses and 300 students, the ratio is:

\[ \frac{8}{300} \]

Now we need to check if these ratios are equal:

To compare these ratios directly, let's check if:

\[ \frac{2}{75} = \frac{8}{300} \]

Cross-multiplying, we have:

\[ 2 \times 300 = 8 \times 75 \]

Calculating both sides:

\[ 600 = 600 \]

Since both values are equal, the proportions are indeed the same.

Thus, the correct relationship between the number of buses and the number of students can be expressed as:

\[ \frac{2}{75} = \frac{8}{300} \]

Therefore, the correct response from the options provided is:

2/75 = 8/300.