How can transformations be used to solve real world problems?

Transformations, im assuming, you mean the ones with graphs on which you move things (ie, x+3; y-10)

imagine setting the table, and you need to add an extra chair for a guest, what do you do?

you transform the x and y of the stuff on one side of the table over, to make room for a new chair and set of tableware. though i dont know if thats a good example