Explanation:
for % problems always try to identify explicitly 100% and/or 1%.
everything else can be easily calculated out of that.
we need to find a 15% increase. of what ? that is the 100% in question.
so,
100% = 50
1% = 100%/100 = 50/100 = 0.5
15% = 1% × 15 = 0.5 × 15 = 7.5
so, 50 + 15% = 50 + 7.5 = 57.5
now, we could simply round (as a half-person or student does not make any sense).
the problem with the rounding is the small number of students overall.
if we round normally, we get 58 students.
but that are 8 students more, and 8 students are (remember, 1% = 0.5)
8/0.5 = 16%
if we round down, we get 57 students.
but that are 7 students more, and 7 students are
7/0.5 = 14%
so, every rounding to "whole students" actuality changes the % significantly.
there is no way to have 15% more students given the small number of students. only 14% more or 16% more.
if you need to give a number, do the normal rounding : 58.
but many greetings to your teacher with my additional comments.
FYI
once you understand the principle behind the % calculation, there are shortcuts to the calculations by combining 2 steps into 1 step :
x% of y is
y×x/100
or
y×0.x
in our case
50×0.15 = 7.5
x% added to y is
y×1.x
in our case
50×1.15 = 57.5
because
50 + 0.15×50 = (1 + 0.15)×50 = 1.15×50 = 57.5