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How would you solve this algebraically? please show me, thanks!

5. The duration of a $80 million portfolio is 12 years. $30 million dollars in new securities are added to the portfolio, increasing the duration of the portfolio to 15 years. What is the duration of the $30 million in new securities? The duration of the enhanced portfolio is the weighted average duration of the $80 million portfolio and the $30 million new securities. The weights are proportional to their market values, or their PVs. Wi- Wg = DU Renhanced port folio WDURW2DUR2 15 years-72.73% x 12 years + 27.27% x DUR2 Solve DUR2. DUR2-23 years 30,000,000+80,000,000-72.73% 30,000,000+30,000,000-27.27%

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