There are two things to solve for; the number of bicycles: b and tricycles: t. Solving for two things requires two equations. You are given enough information to set up:
an equation for number of cycles
b + t = 50
an equation for number of wheels
2b + 3t = 111
Now you can use substitution or elimination to solve for the first variable.
I'll use substitution.
b + t = 50 then b = 50 - t
So sub in (50 - t) for b in the second equation. This combines the two equations into one and makes it in terms of only one variable.
2(50 - t) + 3t = 111
100 - 2t + 3t = 111
100 + t = 111
t = 111 - 100
t = 11
Now use this in either of the equations to find the other variable, b.
11 + b = 50
b = 50 - 11
b = 39
