Finding the Third Proportional to 462 and 616.50

Step by Step Solution

1. Step 1: Write the proportion equation
   462 : 616.50 = 616.50 : x
2. Step 2: Convert to fraction form
   462/616.50 = 616.50/x
3. Step 3: Cross multiply
   462x = 616.50 × 616.50
4. Step 4: Simplify right side
   462x = 380,072.25
5. Step 5: Solve for x
   x = 380,072.25/462
6. Step 6: Final answer
   x = 822.67