Finding the Third Proportional to 83,098 and 178,004

Step by Step Solution

1. Step 1: Write the proportion equation
   83,098 : 178,004 = 178,004 : x
2. Step 2: Convert to fraction form
   83,098/178,004 = 178,004/x
3. Step 3: Cross multiply
   83,098x = 178,004 × 178,004
4. Step 4: Simplify right side
   83,098x = 31,685,424,016
5. Step 5: Solve for x
   x = 31,685,424,016/83,098
6. Step 6: Final answer
   x = 381,301.88