Finding the Third Proportional to 82,106 and 177,030

Step by Step Solution

1. Step 1: Write the proportion equation
   82,106 : 177,030 = 177,030 : x
2. Step 2: Convert to fraction form
   82,106/177,030 = 177,030/x
3. Step 3: Cross multiply
   82,106x = 177,030 × 177,030
4. Step 4: Simplify right side
   82,106x = 31,339,620,900
5. Step 5: Solve for x
   x = 31,339,620,900/82,106
6. Step 6: Final answer
   x = 381,697.09