Finding the Third Proportional to 105,538 and 164,004

Step by Step Solution

1. Step 1: Write the proportion equation
   105,538 : 164,004 = 164,004 : x
2. Step 2: Convert to fraction form
   105,538/164,004 = 164,004/x
3. Step 3: Cross multiply
   105,538x = 164,004 × 164,004
4. Step 4: Simplify right side
   105,538x = 26,897,312,016
5. Step 5: Solve for x
   x = 26,897,312,016/105,538
6. Step 6: Final answer
   x = 254,859.03