Question

There are 620 students and 31 teachers at the Turner Middle School.There are 950 students and 38 teachers at the Green Middle School.
a. Find the ratios of students to teachers at each school. Can you form a proportion with these ratios ? Why or why not?

b. Suppose Green school wants to make its student-teacher ratio close to that at Turner school. How many new teachers would Green have to hire?

c. Can you write a part-to-whole ratio using the data provided? Explain.

Answer 1

We begin with the  Turner Middle School:
Ratio of students to teachers: $\frac{620}{31}$
Green Middle School:
Ratio of students to teachers: $\frac{950}{38}$
Let check that we cannot form a proportion:
$\frac{620}{31}=20\text{ and } \frac{950}{38}=25$
The two ratios are not equals so we cannot form a proportion. 
Let x be the number of teachers that Green have to hire in order to make the two ratios equal. We get the equation:
$\frac{950}{38+x}=\frac{620}{31}\text{ and we solve the equation like this:}\\38+x=\frac{950\times31}{620}=47.5 \text{ and then:}\\x=47.5-38=9.5$

The Green school need to hire 9 teachers. 

Part-to-whole ratio:
Turner Middle School:
 $\frac{620}{31+620}$
Green Middle School:
$\frac{950}{38+950}$

Answer 2

Can someone help with the answer please