Finding the Third Proportional to 82,510 and 178,196

Step by Step Solution

1. Step 1: Write the proportion equation
   82,510 : 178,196 = 178,196 : x
2. Step 2: Convert to fraction form
   82,510/178,196 = 178,196/x
3. Step 3: Cross multiply
   82,510x = 178,196 × 178,196
4. Step 4: Simplify right side
   82,510x = 31,753,814,416
5. Step 5: Solve for x
   x = 31,753,814,416/82,510
6. Step 6: Final answer
   x = 384,848.07