Finding the Third Proportional to 385.88 and 829.38

Step by Step Solution

1. Step 1: Write the proportion equation
   385.88 : 829.38 = 829.38 : x
2. Step 2: Convert to fraction form
   385.88/829.38 = 829.38/x
3. Step 3: Cross multiply
   385.88x = 829.38 × 829.38
4. Step 4: Simplify right side
   385.88x = 687,862.89
5. Step 5: Solve for x
   x = 687,862.89/385.88
6. Step 6: Final answer
   x = 1,782.61