1. **State the problem:** We need to find the cavity and frame area percentages contributing to the real effective RSI using the formula: $$RSI_{r.e.} = (RSI_{cavity} \times A_{cavity}) + (RSI_{frame} \times A_{frame})$$ where $A_{cavity}$ and $A_{frame}$ are the area fractions (percentages as decimals) of cavity and frame respectively, and they satisfy: $$A_{cavity} + A_{frame} = 1$$ 2. **Given data:** - $RSI_{r.e.} = 7.97$ (total effective RSI through cavity) - $RSI_{cavity} = 7.97$ (from cavity assembly) - $RSI_{frame} = 2.25$ (from frame assembly) 3. **Set up the equation:** $$7.97 = 7.97 \times A_{cavity} + 2.25 \times A_{frame}$$ and $$A_{cavity} + A_{frame} = 1$$ 4. **Express $A_{frame}$ in terms of $A_{cavity}$:** $$A_{frame} = 1 - A_{cavity}$$ 5. **Substitute into the RSI equation:** $$7.97 = 7.97 A_{cavity} + 2.25 (1 - A_{cavity})$$ 6. **Simplify:** $$7.97 = 7.97 A_{cavity} + 2.25 - 2.25 A_{cavity}$$ $$7.97 - 2.25 = (7.97 - 2.25) A_{cavity}$$ $$5.72 = 5.72 A_{cavity}$$ 7. **Solve for $A_{cavity}$:** $$A_{cavity} = \frac{5.72}{5.72} = 1$$ 8. **Find $A_{frame}$:** $$A_{frame} = 1 - 1 = 0$$ **Interpretation:** The calculation shows the entire area is cavity (100%) and frame area is 0%, meaning the effective RSI is dominated by the cavity assembly. **Final answer:** - Cavity percentage = 100% - Frame percentage = 0%