Finding the Third Proportional to 82,114 and 177,046

Step by Step Solution

1. Step 1: Write the proportion equation
   82,114 : 177,046 = 177,046 : x
2. Step 2: Convert to fraction form
   82,114/177,046 = 177,046/x
3. Step 3: Cross multiply
   82,114x = 177,046 × 177,046
4. Step 4: Simplify right side
   82,114x = 31,345,286,116
5. Step 5: Solve for x
   x = 31,345,286,116/82,114
6. Step 6: Final answer
   x = 381,728.89