Why did Paul and Barnabas take up collections from the Gentile churches for the believers in Jerusalem?
Paul and Barnabas collected from Gentile churches to relieve the poor Jewish believers in Jerusalem, who had sold their property and become destitute after about twenty years. This met the Jerusalem agreement's condition: Paul and Barnabas would go to Gentiles, the others would stay with the circumcision, and they should remember the poor.
Les explains that the Jerusalem believers had sold all their property, and after twenty years the common fund had run out, leaving them poor and destitute. God did not abandon them; by the Holy Spirit's guidance, Paul and Barnabas were inspired to take collections and offerings as they circulated among the Gentile churches. The Jerusalem leaders agreed Paul and Barnabas could preach to Gentiles without requiring Moses' law or circumcision, but they added the condition to remember the poor. Les also points to Romans 15:25, where Paul goes to Jerusalem to minister to the Jewish believers, and Macedonia and Achaia contributed for the poor saints at Jerusalem, and to 1 Corinthians 16:1 about the collection.