Question: If $QT = b - 17$ and $ST = 2b - 54$, find $QT$ in parallelogram $PQRS$.

1. **State the problem:** We are given a parallelogram $PQRS$ with $QT = b - 17$ and $ST = 2b - 54$. We need to find the value of $QT$. 2. **Important property:** In a parallelogram, the diagonals bisect each other. This means that the segments $QT$ and $ST$ are equal because $T$ is the midpoint of diagonal $QS$. So, we set $QT = ST$. 3. **Set up the equation:** $$b - 17 = 2b - 54$$ 4. **Solve for $b$: Subtract $b$ from both sides: $$b - 17 - b = 2b - 54 - b$$ $$-17 = b - 54$$ Add $54$ to both sides: $$-17 + 54 = b - 54 + 54$$ $$37 = b$$ 5. **Find $QT$: Substitute $b = 37$ into $QT = b - 17$: $$QT = 37 - 17 = 20$$ **Final answer:** $$\boxed{20}$$