I took a vow to feed ten needy people; how much money should I give in charity? Can I spend this vowed money in charity in another country, in Saudi Arabia, for example, given that I live in the USA and do not know how to find poor people there?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.

When a person vows to feed needy people, then he should give them money to buy an enough amount of food, on an average scale—the same quantity of food as given for feeding the needy in religious obligations such as expiations. This amount of food varies between a quarter of a Saa‘ (a Saa‘ is about 3 liters) of food, as is the case for the expiation for missed fast days of Ramadan, and half of a Saa’ of food, as is the case of the fidyah of atha (i.e. expiation for ailment).

Abu Hurayrah said:

While we were sitting with the Prophet, sallallaahu ‘alayhi wa sallam, a man came and said, "O Messenger of Allaah! I have been ruined." The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, asked what was the matter with him. He replied, "I had sexual intercourse with my wife while I was fasting." The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, asked him: "Can you afford to free a slave?" He replied in the negative. The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, asked him: "Can you fast for two successive months?" He again replied in the negative. The Prophet, sallallaahu ‘alayhi wa sallam, asked him: "Can you afford feeding sixty needy persons?" He replied in the negative. The Prophet, sallallaahu ‘alayhi wa sallam, kept silent and, while we were in that state, a big basket full of dates was brought to the Prophet, sallallaahu ‘alayhi wa sallam. He, sallallaahu ‘alayhi wa sallam, asked: "Where is the questioner?" He replied, "I am here." The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said (to him): "Take this (basket of dates) and give it in charity." [Al-Bukhaari and Muslim]

It was reported that the basket had fifteen Saa‘s of dates.

Ka‘b ibn ‘Ujarah said:

"I was carried to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, and lice, in great numbers, were falling on my face. The Prophet, sallallaahu ‘alayhi wa sallam, said: "I have never thought that your suffering reached the extent that I see. Can you afford a sheep (as an expiation for shaving your head)?" I replied in the negative. He, sallallaahu ‘alayhi wa sallam, then said: "Fast for three days or feed six poor persons each with half a Saa‘ of food (and shave your head)." [Al-Bukhaari and Muslim]

One Saa‘ equals  approximately 3 kilograms.

Hence, when the person takes a vow to feed one hundred persons, then he should give 150 or 75 kilograms of food.

It is permissible for the vow-taker to transfer the vowed object to Saudi Arabia or elsewhere, according to the preponderant scholarly opinion. Al-Mirdawi said:

"According to the correct opinion of our school of Fiqh, it is permissible to transfer the object given as an expiation, a vowed object, or a non-specified willed object (i.e. when a person wills to grant something without specifying a certain beneficiary) to any country to which traveling to entails shortening the prayer. Most of the Hanbali scholars adopted this opinion and considered it the correct one." [Al-'Insaf]

Allaah Knows best.