Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
One sacrifice is sufficient on behalf of all the members of a household, no matter how many they are.
Answering your question, we would like to cite the following fatwa published on www.islamqa.info:
At-Tirmidhi narrated that ‘Ata’ ibn Yassar said: I asked Abu Ayyub: How was the sacrifice done at the time of the Messenger of Allah (peace and blessings be upon him)? He said: A man would offer a sheep on behalf of himself and the members of his family, and they would eat some and feed others with some.” (Classed as Sahih by al-Albaani)
It says in Tuhfat al-Ahwadhi:
This hadith clearly states that a single sheep is sufficient on behalf of a man and the members of his household, even if they are many, and that is correct.
Ibn al-Qayyim said: The teaching of the Prophet (peace and blessings of Allah be upon him) was that a sheep is sufficient on behalf of a man and the members of his household, even if they are many in number. (Zad al-Ma`ad)
Al-Shawkani said: In fact a single sheep is sufficient on behalf of the members of a household, even if there are one hundred or more, as is indicated by the Sunnah. (Nayl al-Awtaar)
Shaykh Ibn ‘Uthaymeen said:
There is no limit to how many people may share in the reward. The Prophet (peace and blessings be upon him) offered a sacrifice on behalf of his entire ummah, and a man may offer a single sheep on behalf of himself and the members of his household, even if they are one hundred strong. (Al-Sharh al-Mumti` 5/275)
The Standing Committee was asked: There are twenty-two people in this family, and they have one income and one budget. On `Eid al-Adha they offer a single sacrifice, and I do not know whether that is sufficient or whether they should offer two sacrifices?
They replied: If the family is big but they live in one house, one sacrifice is sufficient for them, but if they offer more than one sacrifice, that is better. (Fatawa al-Lajnah al-Da’imah 11/408)
Allah Almighty knows best.