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.)
75/2 = 8/300
2/75 = 8/300
2/75 ≠ 8/300
2/75 = 300/8
To find the proportion that describes the relationship between the number of buses and the number of students, we need to express the number of students per bus in both cases. We can set up the proportion with the number of buses in the numerator and the number of students in the denominator, ensuring that both sides of the proportion reflect the same relationship (buses to students or students to buses). Since we want to match buses to students, our ratios should be consistent with that.
In the first scenario, 2 buses transport 75 students, so the ratio of buses to students is 2/75.
In the second scenario, 8 buses transport 300 students, so the ratio is 8/300.
To check if these ratios form a proportion, they must contain the same relationship, so they should be equal when we compare them:
2/75 = 8/300
Now, when we cross-multiply, we should get an equality if the ratios form a proportion:
2 * 300 = 8 * 75
600 = 600
Since the multiplied products are equal, the original ratios form a proportion.
Therefore, the correct proportion is:
2/75 = 8/300