1. **State the problem:** We have points R, S, and T on a number line with S between R and T. Given: - $RS = 9y + 2$ - $ST = 3y + 5$ - $RT = 103$ We need to find the value of $y$ and then find the lengths $RS$ and $ST$. 2. **Use the segment addition postulate:** The length of $RT$ is the sum of $RS$ and $ST$: $$RT = RS + ST$$ 3. **Substitute the given expressions:** $$103 = (9y + 2) + (3y + 5)$$ 4. **Simplify the right side:** $$103 = 9y + 2 + 3y + 5$$ $$103 = 12y + 7$$ 5. **Isolate $y$:** $$103 - 7 = 12y$$ $$96 = 12y$$ 6. **Divide both sides by 12:** $$\cancel{12}y = \frac{96}{\cancel{12}}$$ $$y = 8$$ 7. **Find $RS$ and $ST$ by substituting $y=8$:** $$RS = 9(8) + 2 = 72 + 2 = 74$$ $$ST = 3(8) + 5 = 24 + 5 = 29$$ **Final answers:** - $y = 8$ - $RS = 74$ - $ST = 29$