Finding the Third Proportional to 82,422 and 177,984

Step by Step Solution

1. Step 1: Write the proportion equation
   82,422 : 177,984 = 177,984 : x
2. Step 2: Convert to fraction form
   82,422/177,984 = 177,984/x
3. Step 3: Cross multiply
   82,422x = 177,984 × 177,984
4. Step 4: Simplify right side
   82,422x = 31,678,304,256
5. Step 5: Solve for x
   x = 31,678,304,256/82,422
6. Step 6: Final answer
   x = 384,342.82