Finding the Third Proportional to 400.78 and 821.53

Step by Step Solution

1. Step 1: Write the proportion equation
   400.78 : 821.53 = 821.53 : x
2. Step 2: Convert to fraction form
   400.78/821.53 = 821.53/x
3. Step 3: Cross multiply
   400.78x = 821.53 × 821.53
4. Step 4: Simplify right side
   400.78x = 674,913.59
5. Step 5: Solve for x
   x = 674,913.59/400.78
6. Step 6: Final answer
   x = 1,683.99