Finding the Third Proportional to 83,824 and 182,464

Step by Step Solution

1. Step 1: Write the proportion equation
   83,824 : 182,464 = 182,464 : x
2. Step 2: Convert to fraction form
   83,824/182,464 = 182,464/x
3. Step 3: Cross multiply
   83,824x = 182,464 × 182,464
4. Step 4: Simplify right side
   83,824x = 33,293,111,296
5. Step 5: Solve for x
   x = 33,293,111,296/83,824
6. Step 6: Final answer
   x = 397,178.75