Finding the Third Proportional to 82,624 and 178,128

Step by Step Solution

1. Step 1: Write the proportion equation
   82,624 : 178,128 = 178,128 : x
2. Step 2: Convert to fraction form
   82,624/178,128 = 178,128/x
3. Step 3: Cross multiply
   82,624x = 178,128 × 178,128
4. Step 4: Simplify right side
   82,624x = 31,729,584,384
5. Step 5: Solve for x
   x = 31,729,584,384/82,624
6. Step 6: Final answer
   x = 384,023.82