Finding the Third Proportional to 413,385.75 and 585,094.50

Step by Step Solution

1. Step 1: Write the proportion equation
   413,385.75 : 585,094.50 = 585,094.50 : x
2. Step 2: Convert to fraction form
   413,385.75/585,094.50 = 585,094.50/x
3. Step 3: Cross multiply
   413,385.75x = 585,094.50 × 585,094.50
4. Step 4: Simplify right side
   413,385.75x = 342,335,573,930.25
5. Step 5: Solve for x
   x = 342,335,573,930.25/413,385.75
6. Step 6: Final answer
   x = 828,126.21