Udhiyah or animal sacrifice is an act of worship that reminds us of the great sacrifice that Prophet Ibrahim and Isma`il (peace and blessings be upon them) were willing to perform for the sake of Almighty Allah. It is not required for each working member of the house to sacrifice; one sacrifice is sufficient for the whole family.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
According to the vast majority of scholars, sacrifice on `Eid Al-Adha is a highly recommended sunnah; it is not obligatory. Imam Abu Hanifah, however, considers it as obligatory on those who can afford to do so.
The Prophet (peace and blessings be upon him) said, “When the days of Dhul Hijjah draw near and one of you wishes to offer sacrifice, let him not take anything of his hair or nails before the sacrifice has been done!” Those who say sacrifice is a highly recommended ritual base their position on this report: They argue, if sacrifice had been obligatory, then the Prophet (peace and blessings be upon him) would have phrased it more decisively and explicitly, and since he didn’t do so, it shall be deemed as highly recommended.
Now coming to the issue of whether every individual who can afford to sacrifice is required to do so, the answer is that, once again, the majority of scholars are of the view that it is not necessary for everyone to sacrifice; it is enough to sacrifice a single goat or lamb on behalf of an entire family. This is the view of imams such as Malik, Layth, Ahmad, Awza`i, Ishaq ibn Rahawiyah, and others. They base this ruling on the report from the Prophet’s wife `A’ishah (may Allah be pleased with her) that the Prophet (peace and blessings be upon him) sacrificed a goat on behalf of himself and his family. This is further confirmed by a report on the authority of Abu Ayyub, the Prophet’s companion: “During the time of the Prophet (peace and blessings be upon him) it was customary for a person to sacrifice a lamb on behalf of himself and his family; he would feed his family as well as others from its meat.”
In conclusion, it is sufficient for your parents to sacrifice a single goat or lamb on behalf of the entire family.
Excerpted, with slight modifications, from: www.islam.ca