Finding the Third Proportional to 82,834 and 178,784

Step by Step Solution

1. Step 1: Write the proportion equation
   82,834 : 178,784 = 178,784 : x
2. Step 2: Convert to fraction form
   82,834/178,784 = 178,784/x
3. Step 3: Cross multiply
   82,834x = 178,784 × 178,784
4. Step 4: Simplify right side
   82,834x = 31,963,718,656
5. Step 5: Solve for x
   x = 31,963,718,656/82,834
6. Step 6: Final answer
   x = 385,876.80