Finding the Third Proportional to 82,746 and 177,156

Step by Step Solution

1. Step 1: Write the proportion equation
   82,746 : 177,156 = 177,156 : x
2. Step 2: Convert to fraction form
   82,746/177,156 = 177,156/x
3. Step 3: Cross multiply
   82,746x = 177,156 × 177,156
4. Step 4: Simplify right side
   82,746x = 31,384,248,336
5. Step 5: Solve for x
   x = 31,384,248,336/82,746
6. Step 6: Final answer
   x = 379,284.17