In a school, Class A has 24 students with an average height of 160 cm, and Class B has 20 students with an average height of 168 cm. The average height of students in Class C is 165 cm. If the overall average height of all students from Classes A, B and C is 164 cm, find the number of students in Class C.
16
Let the number of students in Class C be \(x\).
Total height of Class A \(= 24 \times 160 = 3840\) cm.
Total height of Class B \(= 20 \times 168 = 3360\) cm.
Total height of Class C \(= 165x\) cm.
Total students \(= 44 + x\), and overall average is 164 cm, so:
\(\frac{3840 + 3360 + 165x}{44 + x} = 164\)
\(7200 + 165x = 7216 + 164x\)
\(x = 16\)
Hence, the number of students in Class C is 16.
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