Finding the Third Proportional to 564 and 616.50

Step by Step Solution

1. Step 1: Write the proportion equation
   564 : 616.50 = 616.50 : x
2. Step 2: Convert to fraction form
   564/616.50 = 616.50/x
3. Step 3: Cross multiply
   564x = 616.50 × 616.50
4. Step 4: Simplify right side
   564x = 380,072.25
5. Step 5: Solve for x
   x = 380,072.25/564
6. Step 6: Final answer
   x = 673.89