In order to determine the number of people which won something, it is necessary to write the following system of equations:
x + y = 165
y/x = 12/3
x is the people won and y the people lost.
The first equation represents tha total number of people in the event.
The second equation represents the ratio of losing tickets to winning people.
First, solve the second equation for y, and then replace the expression for y into the first equation:
y = 12/3 x
x + 12/3 x = 165
next, solve the last equation for x:
(3+12)/3 x = 165
15/3 x = 165
5x = 165
x = 165/5
x = 33
x is the number of people who won something in the event.
Hence, the number of people was 33