Question

The ratio of students to teachers at a school is 19:1. How many students are there in each total number of people? a. 100 people b. 280 people c. 440 people d. 760 people

Answer 1

To answer this question, we need to find the part-to-whole comparison in this ratio.

We can find this as follows:

1. We have 19 students for every 1 teacher. Then, the whole is 20 people.

2. Now we can find that:

`r_{\text{students}}=(19)/(20),r_{\text{teachers}}=(1)/(20)`

Thus, in fraction form, taking into account the part-to-whole comparison, we have that the students represent 19/20 of the total of a group of people. Then, for each case given, we need to multiply them by this fraction so that we get the total number of students for each total number of people:

For 100 people:

`T_{\text{students}}=(19)/(20)\cdot100=(19\cdot100)/(20)\Rightarrow T_(students)=95`

For 280 people:

`T_{\text{students}}=(19)/(20)\cdot280=(19\cdot280)/(20)\Rightarrow T_(students)=266`

For 440 people:

`T_{\text{students}}=(19)/(20)\cdot440\Rightarrow T_(students)=418`

For 760 people:

`T_{\text{students}}=(19)/(20)\cdot760\Rightarrow T_(students)=722`

Therefore, we have that:

• For 100 people, we have 95 students.

,

• For 280 people, we have 266 students.

,

• For 440 people, we have 418 students.

,

• For 760 people, we have 722 students.