Question

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1.

What is the present number of teachers?

Answer 1

Answer: 15

Explanation:

Given: The present ratio of students to teachers at a certain school is
`30` to
`1`. If the student enrollment were to increase by
`50` students and the number of teachers were to increase by
`5`, the ratio of students to teachers would then be
`25` to
`1`.

To Find: What is the present number of teachers.

Solution:

let the number of teachers in schools are
`=\text{x}`

As the current ratio of students to teachers is
`30` to
`1`

Number of students in school are
`=30\text{x}`

Now,

If number of student enrollment and teachers were to increase by
`50` and
`5` respectively.

New number of students in school would be
`=30\text{x}+50`

New number of teacher in school would be
`\text{x}+5`

new ratio of students to teachers is
`25:1`

`\frac{30\text{x}+50}{\text{x}+5}=(25)/(1)`

`30\text{x}+50=25\text{x}+125`

`5\text{x}=75`

`\text{x}=15`

Hence the number of teachers in school is
`15`