"The Four Hundred" list was a phrase coined by Ward McAllister, a rich New Yorker who thought that there were exactly 400 people in New York who mattered. This elite was strictly limited, in his opinion, which means that people within this circle held up to each other, disregarding the outside world and always trying to become better than the neighbor: they wanted to spend more, live in bigger homes, have more expensive cars, all in hope to better show off their top position on the social ladder.
The "four-hundred list" is a list of 400 important people that were the elite in New York during the Gilded Age.
"keeping up with the joneses" is an idiom referring to the comparison to one's neighbor as a benchmark for social class or the accumulation of material goods.
The idea of not being in that list is what could have contributed to create the "keeping up with the Joneses" idiom. You had to have prestige and material things to be in the "four-hundred list" and that meant having more than others (the "Joneses"). The "keeping up" would mean to tolerate others having less than you do. For example: a neighbour.
I think the answer is that Sarah should look up words she doesn't know for chapter titles, headings and first paragraphs and write the main idea in her own words.
