Finding the Third Proportional to 419.63 and 693.56

Step by Step Solution

1. Step 1: Write the proportion equation
   419.63 : 693.56 = 693.56 : x
2. Step 2: Convert to fraction form
   419.63/693.56 = 693.56/x
3. Step 3: Cross multiply
   419.63x = 693.56 × 693.56
4. Step 4: Simplify right side
   419.63x = 481,028.94
5. Step 5: Solve for x
   x = 481,028.94/419.63
6. Step 6: Final answer
   x = 1,146.33