Finding the Third Proportional to 81,742 and 176,006

Step by Step Solution

1. Step 1: Write the proportion equation
   81,742 : 176,006 = 176,006 : x
2. Step 2: Convert to fraction form
   81,742/176,006 = 176,006/x
3. Step 3: Cross multiply
   81,742x = 176,006 × 176,006
4. Step 4: Simplify right side
   81,742x = 30,978,112,036
5. Step 5: Solve for x
   x = 30,978,112,036/81,742
6. Step 6: Final answer
   x = 378,974.24