From both the IATA and the AFIP websites the dollar thresholds are different for different aged children.
From the IATA Website:
Currency Export regulations:
Local currency (Argentine Peso-ARS) and foreign currencies: prohibited unless exportation is made through authorized financial and foreign exchange entities, for amounts above:
-USD 10,000.- (or equivalent) for travelers aged over 21 or independent minors; or
-USD 2,000.- (or equivalent) for travelers aged between 16 and 21 years; or
-USD 1,000.- (or equivalent) for travelers aged under 16 years.
From the AFIP Website:
Exit of bills, coins and precious metals from the Argentine territory (RG 2705)
The travelers, older than 16 years old and emancipated, can exit the Argentine territory with a maximum amount of ten thousand American Dollars ($10,000) or its equivalent in precious metals, cash, traveler’s checks and/or other currency.
However, the amount shall be of five thousand American Dollars ($5,000) or its equivalent in precious metals, cash, traveler’s checks and/or other currency in the case of travelers under the age of 16 years old and not emancipated.
These limits shall be applicable to each traveler or crew. The currency exchange shall be made using the exchange rate of the day prior to the exit informed by the Bank of the Argentine Nation. The legal tender is excluded from this limitation, without prejudice of the Customs declaration (Form OM-2250-A), when the total amount that will exit the country is equal or above ten thousand American Dollars ($10,000).
The currency exchange shall be made using the sellers’ exchange rate of the day prior to the departure informed by the Bank of the Argentine Nation.
As a retired customs officer (US) I like the Argentine requirement of a certified/notarized letter from the parent not traveling with the children, giving permission. You'd be somewhat surprised (l know I was when I first started working for CBP) at the volume of phone calls received at the border regarding one parent taking their children outside of the U.S. without permission - especially with divorced parents. I have a friend going through a nasty divorce. Her soon to be ex-husband is only allowed supervised visitation of his daughter (only at his parent's house, only for a few hours a week). He has stated he will "take" his daughter to Canada whenever he wants...oh snap that won't be a good thing - both the U.S. and Canadian Customs and Immigration Officials are already and are waiting for his very short visit to Canada and return to the U.S. The welfare and protection of children at the border has become a very high priority - not that it wasn't before - but it really isn't something you'd want to try now.