Bite-sized brain teaser to solve in a minute or less.
Students and Teachers
A school maintains a student-to-teacher ratio of 20:1. However, after 5 teachers unexpectedly leave, the ratio increases to 25:1.
How many students are enrolled at the school?
Solution
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Let: s = number of students t = the original number of teachers
Then the number of students would be: s = 20t
After 5 teachers leave: The new number of teachers = t - 5 The student-to-teacher ratio = 25 : 1
Therefore: s / (t - 5) = 25
Since s = 20t, substitute this into the ratio equation: 20t / (t - 5) = 25 20t = 25 (t - 5) 20t = 25t -125 125 = 25t - 20t 125 = 5t t = 25
Calculate the number of students: s = 20t s = 20 x 25 s = 500 There are 500 students enrolled at the school. |
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