The correct answer to this open question is the following.
The tycoons used the "Gospel of Wealth" and Social Darwinism to explain keeping the wealthy richer and keeping the poor even poorer the following way.
Social Darwinism and the Gospel of Wealth were used to defend the dominant economic and social order after the civil war to 1900 in different ways.
"The Gospel of Wealth," was an essay written by the philanthropic and entrepreneur Andrew Carnegie in 1889. In that document, Carnegie gave some suggestions and advice to other rich men about the way they should live their lives.
This, because Social Darwinism had been influenced the lives of people in the late-nineteenth-century. Social Darwinism was a “type of ideology” that wanted to prove the superiority of Anglo-Saxons over other races. The supporters of this way of thinking considered the assumption that white Northern Europeans were superior to all other groups. The social scientists that believed in thos theories supported the oppression of classes, justifying racism instead of trying to find or at least understand the social differences. The supporters of Social Darwinism did not approve of the government programs directed to help the ones in need, considered that the poor were born to be poor in this life as a natural condition.
Then, enters Andrew Carnegie with his Gospel of Wealth. In the mentioned essay, Carnegie elaborated on philanthropic projects intending to benefit poor people. Carnegie intended to change the extreme ideas of Social Darwinism. He considered that the rich should be thankful for their wealth and a way to show it was helping the poor. Not many rich families agreed with Carnegie. They preferred the accumulation of wealth instead of the support of social programs.