Write a real world problem that can be modeled by the equation 1.25x=0.75x+50

This is not really an equation that can be used to model anything as there is only one variable. see this.
1.25x-0.75x = 50
0.5x = 50
x=100
It can be solved and therefore does not have an input and an output required to model anything

1) The parking in A-park costs 1.25 per hour; however, if you get a membership for 50 dollars, it only costs 0.75 per hour. At what hour would the cost of parking be equal no matter whether you get a membership?
2) 
1/6 x = 1/12 x + 5/3
3)
0.1x = 0.01x + 2.25