Finding the Third Proportional to 82,080 and 175,824

Step by Step Solution

1. Step 1: Write the proportion equation
   82,080 : 175,824 = 175,824 : x
2. Step 2: Convert to fraction form
   82,080/175,824 = 175,824/x
3. Step 3: Cross multiply
   82,080x = 175,824 × 175,824
4. Step 4: Simplify right side
   82,080x = 30,914,078,976
5. Step 5: Solve for x
   x = 30,914,078,976/82,080
6. Step 6: Final answer
   x = 376,633.52