Finding the Third Proportional to 82,460 and 178,042

Step by Step Solution

1. Step 1: Write the proportion equation
   82,460 : 178,042 = 178,042 : x
2. Step 2: Convert to fraction form
   82,460/178,042 = 178,042/x
3. Step 3: Cross multiply
   82,460x = 178,042 × 178,042
4. Step 4: Simplify right side
   82,460x = 31,698,953,764
5. Step 5: Solve for x
   x = 31,698,953,764/82,460
6. Step 6: Final answer
   x = 384,416.13