Finding the Third Proportional to 102,649 and 164,514

Step by Step Solution

1. Step 1: Write the proportion equation
   102,649 : 164,514 = 164,514 : x
2. Step 2: Convert to fraction form
   102,649/164,514 = 164,514/x
3. Step 3: Cross multiply
   102,649x = 164,514 × 164,514
4. Step 4: Simplify right side
   102,649x = 27,064,856,196
5. Step 5: Solve for x
   x = 27,064,856,196/102,649
6. Step 6: Final answer
   x = 263,664.10