If two buses are needed to transport 75 students to the aquarium and eight 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
Let's define:
b = number of buses
s = number of students
We know that the relationship between the number of buses and the number of students is given by the ratio of 8 buses to 300 students. So, we can write:
8 buses/300 students = b buses/s students
To find the relationship between the number of buses and the number of students needed to transport 75 students, we can solve for b. Rearranging the equation, we have:
b buses = (8 buses/300 students) * (s students)
We have the information that two buses are needed to transport 75 students, so we can substitute b = 2 buses and s = 75 students:
2 buses = (8 buses/300 students) * (75 students)
Now we can solve for (75 students) by multiplying both sides of the equation by (300 students/8 buses), canceling out units on the right side:
2 buses * (300 students/8 buses) = (75 students)
Simplifying the right side, we get:
2 buses * 37.5 students/bus = 75 students
So, the proportion that describes the relationship between the number of buses and the number of students is:
2 buses : 75 students
To find the proportion that describes the relationship between the number of buses and the number of students, we can set up a ratio.
Let x represent the number of buses needed to transport the 75 students.
The given information states that 8 buses can transport 300 students. We can set up the proportion:
8 buses / 300 students = x buses / 75 students
To not reduce the ratio to its lowest terms, we leave it in this form:
8 buses / 300 students = x buses / 75 students
To find the proportion that describes the relationship between the number of buses and the number of students, we need to compare the two scenarios given:
1) Two buses transporting 75 students
2) Eight buses transporting 300 students
The proportion can be set up as:
(2 buses / 8 buses) = (75 students / 300 students)
To keep the ratios from being reduced to their lowest terms, we leave both sides of the equation as is.
Therefore, the proportion that describes the relationship between the number of buses and the number of students is:
(2 buses / 8 buses) = (75 students / 300 students)