The choice Walter makes to give Travis more money than he needs for school has bearing on Walter's character and also serves to subtly imply his state of desperation.
Walter does not like his job as a chauffeur. He feels that it is beneath him to serve someone else in this capacity. He also does not get paid very well. Both of these circumstances make Walter's sense of his own position rather painful, especially in relation to his son.
He yearns deeply to change his position. He is willing to act recklessly to change things, as we see Walter's choice to give Travis extra money. In doing this Walter makes a play to change himself in his son's eyes at least, asserting his manhood at the same time.
In summation, Walter gives Travis more money than he needs as a demonstration of his feelings, his rather desperate need to find a position of greater pride and dignity.
Ruth continues to scramble Walter's eggs because he is trying to tell Ruth about his dream and she tells him to eat his eggs. He wants to talk and dream of a better life; she wants him to face reality and deal with his present world. This makes him frustrated, makes him feel like she doesn't support him. Therefore, their relationship is one that lacks respect for each other and also demonstrates the despair they both feel living in a small apartment with not enough space for everyone. She is tired of listening to his absurdity because he has never been able to fulfill any of his dreams. One of the reasons Ruth tells Travis to get his mind off the money that is coming the next day is because it's mama's money and everyone in the house is dreaming about what they can do with the check and seem to have a lack of regard for mama. She is trying to teach Travis that money is not everything, although Travis has dreams for the use of the money himself.
Walter gives his son the fifty cents he needs for school so Travis doesn't feel like his dad cannot afford to give him things. Ironically, he needs to ask Ruth for money to get to work. Therefore, this demonstrates Walter's need to be a man and to show Travis that he can provide for his family.
The rift indicated between Walter and Ruth suggests that Ruth as well as mama is a good Christian woman and she does not want her husband opening a liquor store because alcohol is a symbol of immorality, infidelity and not consistent with orthodox Christian values.
In their marriage there is some conflict with their respective religious values even though theoretically a marriage is a traditional, religious institution.