Finding the Third Proportional to 83,142 and 178,096.50

Step by Step Solution

1. Step 1: Write the proportion equation
   83,142 : 178,096.50 = 178,096.50 : x
2. Step 2: Convert to fraction form
   83,142/178,096.50 = 178,096.50/x
3. Step 3: Cross multiply
   83,142x = 178,096.50 × 178,096.50
4. Step 4: Simplify right side
   83,142x = 31,718,363,312.25
5. Step 5: Solve for x
   x = 31,718,363,312.25/83,142
6. Step 6: Final answer
   x = 381,496.28