Finding the Third Proportional to 82,858 and 177,326

Step by Step Solution

1. Step 1: Write the proportion equation
   82,858 : 177,326 = 177,326 : x
2. Step 2: Convert to fraction form
   82,858/177,326 = 177,326/x
3. Step 3: Cross multiply
   82,858x = 177,326 × 177,326
4. Step 4: Simplify right side
   82,858x = 31,444,510,276
5. Step 5: Solve for x
   x = 31,444,510,276/82,858
6. Step 6: Final answer
   x = 379,498.78