no. of pupils: u [ = 1 unit ]
avg h = 143
total h = 143u

after F joins
no. of pupils: u + 1
avg h = 148
total h = 148 x (u+1) = 148u + 148

148u + 148 - 143u = 168
u = 4

in the end, 5 pupils


...

Non algebra method :

Fred is 168cm tall. Now the average is 148cm.

168cm - 148cm = 20cm

So we can treat it like Fred 'gave' 20cm of his height to the other pupils so they all even out to 148cm.

Previously the average is 143cm.

148cm - 143cm = 5cm

Each pupil 'gained' 5cm from Fred.

20cm ÷ 5cm gained per pupil
= 4

So there were 4 pupils before Fred joined


Total pupils in the end
= 4 + 1 = 5

Thanks J!

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