Finding the Third Proportional to 463.50 and 698.50

Step by Step Solution

1. Step 1: Write the proportion equation
   463.50 : 698.50 = 698.50 : x
2. Step 2: Convert to fraction form
   463.50/698.50 = 698.50/x
3. Step 3: Cross multiply
   463.50x = 698.50 × 698.50
4. Step 4: Simplify right side
   463.50x = 487,902.25
5. Step 5: Solve for x
   x = 487,902.25/463.50
6. Step 6: Final answer
   x = 1,052.65