How Can Sinners Be Made Righteous While God Maintains His Justice?

The bible says the wages of sin is death. How can sinners be made righteous while god maintains his justice? Would it be just for a judge to let some sort of crime happen and go unpunished? No, it would not be just. God must remain just in order to remain holy and perfect. So what does god do with your sin? Well, he applies it to jesus. He takes our sin and punishes jesus to maintain his justice. Then god gives the righteousness of christ to us through faith, making us holy. This really is good news. Why is paul not ashamed of the gospel? Because it's god's provision for sinners to become righteous