Finding the Third Proportional to 414,391 and 584,910

Step by Step Solution

1. Step 1: Write the proportion equation
   414,391 : 584,910 = 584,910 : x
2. Step 2: Convert to fraction form
   414,391/584,910 = 584,910/x
3. Step 3: Cross multiply
   414,391x = 584,910 × 584,910
4. Step 4: Simplify right side
   414,391x = 342,119,708,100
5. Step 5: Solve for x
   x = 342,119,708,100/414,391
6. Step 6: Final answer
   x = 825,596.38