The average weight of the students in a class is 56 kg. If five more students whose average weight is 58 kg, join the class, the average weight of the students increases by 0.5 kg. What was the original number of students in the class?

Let the original number of students be n.
Original total weight = 56n

Five new students join, with an average weight of 58 kg.
Total weight of new students = 5×58=290 kg
New total number of students = n+5
New average weight = 56+0.5=56.5 kg

Set up the equation:

n+5
56n+290
​
=56.5
56n+290=56.5(n+5)
56n+290=56.5n+282.5
290−282.5=56.5n−56n
7.5=0.5n
n=
0.5
7.5
​
=15
Thus, the original number of students was 15.