Answer: 15
Step-by-step explanation:
Given: The present ratio of students to teachers at a certain school is [tex]30[/tex] to [tex]1[/tex]. If the student enrollment were to increase by [tex]50[/tex] students and the number of teachers were to increase by [tex]5[/tex], the ratio of students to teachers would then be [tex]25[/tex] to [tex]1[/tex].
To Find: What is the present number of teachers.
Solution:
let the number of teachers in schools are [tex]=\text{x}[/tex]
As the current ratio of students to teachers is [tex]30[/tex] to [tex]1[/tex]
Number of students in school are [tex]=30\text{x}[/tex]
Now,
If number of student enrollment and teachers were to increase by [tex]50[/tex] and [tex]5[/tex] respectively.
New number of students in school would be [tex]=30\text{x}+50[/tex]
New number of teacher in school would be [tex]\text{x}+5[/tex]
new ratio of students to teachers is [tex]25:1[/tex]
[tex]\frac{30\text{x}+50}{\text{x}+5}=\frac{25}{1}[/tex]
[tex]30\text{x}+50=25\text{x}+125[/tex]
[tex]5\text{x}=75[/tex]
[tex]\text{x}=15[/tex]
Hence the number of teachers in school is [tex]15[/tex]
