Finding the Third Proportional to 82,856 and 177,320

Step by Step Solution

1. Step 1: Write the proportion equation
   82,856 : 177,320 = 177,320 : x
2. Step 2: Convert to fraction form
   82,856/177,320 = 177,320/x
3. Step 3: Cross multiply
   82,856x = 177,320 × 177,320
4. Step 4: Simplify right side
   82,856x = 31,442,382,400
5. Step 5: Solve for x
   x = 31,442,382,400/82,856
6. Step 6: Final answer
   x = 379,482.26