Finding the Third Proportional to 82,002 and 177,606

Step by Step Solution

1. Step 1: Write the proportion equation
   82,002 : 177,606 = 177,606 : x
2. Step 2: Convert to fraction form
   82,002/177,606 = 177,606/x
3. Step 3: Cross multiply
   82,002x = 177,606 × 177,606
4. Step 4: Simplify right side
   82,002x = 31,543,891,236
5. Step 5: Solve for x
   x = 31,543,891,236/82,002
6. Step 6: Final answer
   x = 384,672.22