The present ratio of students to teachers at a certain school is 30 to 1. If…
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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 was to increase by 5, the ratio of the students to teachers would then be 25 to 1, what is the present number of teachers?
- A.
18
- B.
20
- C.
15
- D.
22
Attempted by 72 students.
Show answer & explanation
Correct answer: C
The correct number of teachers is 15. (Note: While option C is highlighted in the image, the math indicates 15 is the correct result).
Detailed Explanation
We can solve this using the proportionality concept mentioned earlier:
Define the variables:
Let the current number of teachers be t.
Since the current ratio of students to teachers is 30:1, the current number of students is 30t.
Set up the equation based on the changes:
New number of students = 30t + 50
New number of teachers = t + 5
The new ratio is 25:1. Therefore:
(30t + 50) / (t + 5) = 25
Solve for t:
30t + 50 = 25 * (t + 5)
30t + 50 = 25t + 125
30t - 25t = 125 - 50
5t = 75
t = 15