Question

The table gives the numbers of teachers and students in grades 6 to 8 at Earhart Middle School.

Grade Teachers Students

6 grade , teacher 1 , student 25

7 garde , teacher 2 , student 50

8 grade , teacher 3 , student 75


Which teacher-to-student ratio maintains the proportional relationship described in the table?



Teachers Students

5 teachers, students 125


Teachers Students

4 teachers , students 120


Teachers Students

4teachers ,students 100


Teachers Students

6 teachers ,students 130


Teachers Students

7 teachers,students 125

im sorry if its like this i havent been having a good day

Answer 1

5 teachers, students 125

4 teachers, students 100

Explanation:

step 1

Find teacher-to-student ratio in the table

To determine the ratio, divide the number of teachers by the number of students

6 grade

`(1)/(25)`

7 grade

`(2)/(50)`

Simplify

`(1)/(25)`

8 grade

`(3)/(75)`

Simplify

`(1)/(25)`

step 2

Verify each case

case a) 5 teachers, students 125

`ratio=(5)/(125)`

Simplify

Divide by 5 both numerator and denominator

`ratio=(1)/(25)`

Compare with the ratio described in the table

`(1)/(25)=(1)/(25)`

therefore

This ratio maintains the proportional relationship described in the table

case b) 4 teachers, students 120

`ratio=(4)/(120)`

Simplify

Divide by 4 both numerator and denominator

`ratio=(1)/(30)`

Compare with the ratio described in the table

`(1)/(30)\\eq (1)/(25)`

therefore

This ratio not maintains the proportional relationship described in the table

case c) 4 teachers, students 100

`ratio=(4)/(100)`

Simplify

Divide by 4 both numerator and denominator

`ratio=(1)/(25)`

Compare with the ratio described in the table

`(1)/(25)=(1)/(25)`

therefore

This ratio maintains the proportional relationship described in the table

case d) 6 teachers, students 130

`ratio=(6)/(130)`

Simplify

`ratio=(3)/(65)`

Compare with the ratio described in the table

`(3)/(65)\\eq(1)/(25)`

therefore

This ratio not maintains the proportional relationship described in the table

case e) 7 teachers, students 125

`ratio=(7)/(125)`

Compare with the ratio described in the table

`(7)/(125)\\eq(1)/(25)`

therefore

This ratio not maintains the proportional relationship described in the table