Finding the Third Proportional to 102,164 and 164,046

Step by Step Solution

1. Step 1: Write the proportion equation
   102,164 : 164,046 = 164,046 : x
2. Step 2: Convert to fraction form
   102,164/164,046 = 164,046/x
3. Step 3: Cross multiply
   102,164x = 164,046 × 164,046
4. Step 4: Simplify right side
   102,164x = 26,911,090,116
5. Step 5: Solve for x
   x = 26,911,090,116/102,164
6. Step 6: Final answer
   x = 263,410.69