Finding the Third Proportional to 82,089 and 177,003

Step by Step Solution

1. Step 1: Write the proportion equation
   82,089 : 177,003 = 177,003 : x
2. Step 2: Convert to fraction form
   82,089/177,003 = 177,003/x
3. Step 3: Cross multiply
   82,089x = 177,003 × 177,003
4. Step 4: Simplify right side
   82,089x = 31,330,062,009
5. Step 5: Solve for x
   x = 31,330,062,009/82,089
6. Step 6: Final answer
   x = 381,659.69