Finding the Third Proportional to 413,406 and 585,123.75

Step by Step Solution

1. Step 1: Write the proportion equation
   413,406 : 585,123.75 = 585,123.75 : x
2. Step 2: Convert to fraction form
   413,406/585,123.75 = 585,123.75/x
3. Step 3: Cross multiply
   413,406x = 585,123.75 × 585,123.75
4. Step 4: Simplify right side
   413,406x = 342,369,802,814.06
5. Step 5: Solve for x
   x = 342,369,802,814.06/413,406
6. Step 6: Final answer
   x = 828,168.44