Question

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

Answer 1

Answer:

5 teachers, students 125

4 teachers, students 100

Step-by-step 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

$\frac{1}{25}$

7 grade

$\frac{2}{50}$

Simplify

$\frac{1}{25}$

8 grade

$\frac{3}{75}$

Simplify

$\frac{1}{25}$

step 2

Verify each case

case a) 5 teachers, students 125

$ratio=\frac{5}{125}$

Simplify

Divide by 5 both numerator and denominator

$ratio=\frac{1}{25}$

Compare  with the ratio described in the table

$\frac{1}{25}=\frac{1}{25}$

therefore

This ratio maintains the proportional relationship described in the table

case b) 4 teachers, students 120

$ratio=\frac{4}{120}$

Simplify

Divide by 4 both numerator and denominator

$ratio=\frac{1}{30}$

Compare  with the ratio described in the table

$\frac{1}{30}\neq \frac{1}{25}$

therefore

This ratio not maintains the proportional relationship described in the table

case c) 4 teachers, students 100

$ratio=\frac{4}{100}$

Simplify

Divide by 4 both numerator and denominator

$ratio=\frac{1}{25}$

Compare  with the ratio described in the table

$\frac{1}{25}=\frac{1}{25}$

therefore

This ratio maintains the proportional relationship described in the table

case d) 6 teachers, students 130

$ratio=\frac{6}{130}$

Simplify

$ratio=\frac{3}{65}$

Compare  with the ratio described in the table

$\frac{3}{65}\neq\frac{1}{25}$

therefore

This ratio not maintains the proportional relationship described in the table

case e) 7 teachers, students 125

$ratio=\frac{7}{125}$

Compare  with the ratio described in the table

$\frac{7}{125}\neq\frac{1}{25}$

therefore

This ratio not maintains the proportional relationship described in the table