In 2007, an Israeli historian named Gur Alroey published a study about the choices and difficulties faced by Jewish immigrants from Russia. Based on published prices from that era, he estimated the actual monetary cost of getting from Russia to America, for a family that – remarkably – exactly resembled the Dubersteins when they immigrated in 1900:
“…the cost of migration to the US for a family of ten between 1900 and 1908 (parents and eight children, four above 12 years old, and four under 12) is estimated at 600 rubles for passage on the ship, 15 rubles to obtain a passport or cross the border illegally, 120 rubles for the train fare (depending on the destination and distance), and 10 rubles for accommodations and food. Thus the total cost for the whole family is estimated at 745 rubles ($372.50, equivalent to approximately $7,600 today). For the average Jewish family, whose annual income was 500-600 rubles ($250-$300), it was a fortune.”
Like Alroey's family, the Dubersteins came over as a family of 10, as passengers on the Furst Bismarck, sailing out of Hamburg on May 17, 1900. Two of the children (Anna and Bertha) were over 12, the rest under 12. We can only wonder, given the available information, how they managed to raise the necessary funds to finance the trip. (Alroey makes the point that the high cost was typically the reason male breadwinners came first, sending for their families as they made enough to pay for their passage.)
One important point, often forgotten: Immigrants like the Dubersteins needed passports, not to get into the U.S., but to (legally) get out of Russia. Getting a passport was a complicated and difficult process, so many elected to cross the Russian border illegally, using what we today call "coyotes," or smugglers. This was dangerous, and could involve costly bribes and fees, but was often preferable to dealing with the Russian bureaucracy.