The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is
99
Let the shifts be \(13x\) and \(9x\).
\(\dfrac{13x-21}{9x+21}=\dfrac{19}{14}\)
\(182x-294=171x+399 \Rightarrow 11x=693 \Rightarrow x=63\)
Morning = \(819-21=798\), Afternoon = \(567+21=588\).
New students \(3y\) and \(8y\): \(\dfrac{798+3y}{588+8y}=\dfrac{5}{4}\)
\(3192+12y=2940+40y \Rightarrow 28y=252 \Rightarrow y=9\)
New students = \(3y+8y=11\times 9=99\). Check: \(825:660=5:4\).
Hence, 99.
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