Finding the Third Proportional to 82,409 and 179,506

Step by Step Solution

1. Step 1: Write the proportion equation
   82,409 : 179,506 = 179,506 : x
2. Step 2: Convert to fraction form
   82,409/179,506 = 179,506/x
3. Step 3: Cross multiply
   82,409x = 179,506 × 179,506
4. Step 4: Simplify right side
   82,409x = 32,222,404,036
5. Step 5: Solve for x
   x = 32,222,404,036/82,409
6. Step 6: Final answer
   x = 391,005.89