Being temple attending Jews, the Bereans may have asked Paul, “why do we need the blood of Jesus to cover our sins? We have the yearly offerings to atone for us.” Paul probably answered them using scriptures they would have been familiar with.
Isaiah 1:10-12 Amplified Bible, Classic Edition
10 Hear [O Jerusalem] the word of the Lord, you rulers or judges of [another] Sodom! Give ear to the law and the teaching of our God, you people of [another] Gomorrah!
11 To what purpose is the multitude of your sacrifices to Me [unless they are the offering of the heart]? says the Lord. I have had enough of the burnt offerings of rams and the fat of fed beasts [without obedience]; and I do not delight in the blood of bulls or of lambs or of he-goats [without righteousness].
12 When you come to appear before Me, who requires of you that your [unholy feet] trample My courts?
Ecclesiastes 5:1 International Children’s Bible
5 Be careful when you go to worship at the Temple. It is better to listen than to offer foolish sacrifices. People who do this don’t even know they are doing wrong.
Micah 6:6-8 Good News Translation. What the Lord Requires
6 What shall I bring to the Lord, the God of heaven, when I come to worship him? Shall I bring the best calves to burn as offerings to him? 7 Will the Lord be pleased if I bring him thousands of sheep or endless streams of olive oil? Shall I offer him my first-born child to pay for my sins? 8 No, the Lord has told us what is good. What he requires of us is this: to do what is just, to show constant love, and to live in humble fellowship with our God.
Ultimately Paul would have pointed them to Jesus their true savior.
Psalm 40:6-8 New International Version
6 Sacrifice and offering you did not desire but my ears you have opened burnt offerings and sin offerings you did not require.
7 Then I said, “Here I am, I have come it is written about me in the scroll.
8 I desire to do your will, my God; your law is within my heart.”
Jesus alone has the power to save mankind. When Paul introduced Jesus to the Bereans he used Old Testament scriptures, which ones would you use?