Finding the Third Proportional to 269,084 and 416,384

Step by Step Solution

1. Step 1: Write the proportion equation
   269,084 : 416,384 = 416,384 : x
2. Step 2: Convert to fraction form
   269,084/416,384 = 416,384/x
3. Step 3: Cross multiply
   269,084x = 416,384 × 416,384
4. Step 4: Simplify right side
   269,084x = 173,375,635,456
5. Step 5: Solve for x
   x = 173,375,635,456/269,084
6. Step 6: Final answer
   x = 644,317.89