Finding the Third Proportional to 414,075 and 582,952.50

Step by Step Solution

1. Step 1: Write the proportion equation
   414,075 : 582,952.50 = 582,952.50 : x
2. Step 2: Convert to fraction form
   414,075/582,952.50 = 582,952.50/x
3. Step 3: Cross multiply
   414,075x = 582,952.50 × 582,952.50
4. Step 4: Simplify right side
   414,075x = 339,833,617,256.25
5. Step 5: Solve for x
   x = 339,833,617,256.25/414,075
6. Step 6: Final answer
   x = 820,705.47