Finding the Third Proportional to 414,027 and 585,967.50

Step by Step Solution

1. Step 1: Write the proportion equation
   414,027 : 585,967.50 = 585,967.50 : x
2. Step 2: Convert to fraction form
   414,027/585,967.50 = 585,967.50/x
3. Step 3: Cross multiply
   414,027x = 585,967.50 × 585,967.50
4. Step 4: Simplify right side
   414,027x = 343,357,911,056.25
5. Step 5: Solve for x
   x = 343,357,911,056.25/414,027
6. Step 6: Final answer
   x = 829,312.85