Finding the Third Proportional to 413,433 and 585,159.75

Step by Step Solution

1. Step 1: Write the proportion equation
   413,433 : 585,159.75 = 585,159.75 : x
2. Step 2: Convert to fraction form
   413,433/585,159.75 = 585,159.75/x
3. Step 3: Cross multiply
   413,433x = 585,159.75 × 585,159.75
4. Step 4: Simplify right side
   413,433x = 342,411,933,020.06
5. Step 5: Solve for x
   x = 342,411,933,020.06/413,433
6. Step 6: Final answer
   x = 828,216.26