Finding the Third Proportional to 477.56 and 563.06

Step by Step Solution

1. Step 1: Write the proportion equation
   477.56 : 563.06 = 563.06 : x
2. Step 2: Convert to fraction form
   477.56/563.06 = 563.06/x
3. Step 3: Cross multiply
   477.56x = 563.06 × 563.06
4. Step 4: Simplify right side
   477.56x = 317,039.38
5. Step 5: Solve for x
   x = 317,039.38/477.56
6. Step 6: Final answer
   x = 663.87