Finding the Third Proportional to 82,769 and 178,661

Step by Step Solution

1. Step 1: Write the proportion equation
   82,769 : 178,661 = 178,661 : x
2. Step 2: Convert to fraction form
   82,769/178,661 = 178,661/x
3. Step 3: Cross multiply
   82,769x = 178,661 × 178,661
4. Step 4: Simplify right side
   82,769x = 31,919,752,921
5. Step 5: Solve for x
   x = 31,919,752,921/82,769
6. Step 6: Final answer
   x = 385,648.65