Finding the Third Proportional to 53,820 and 83,538

Step by Step Solution

1. Step 1: Write the proportion equation
   53,820 : 83,538 = 83,538 : x
2. Step 2: Convert to fraction form
   53,820/83,538 = 83,538/x
3. Step 3: Cross multiply
   53,820x = 83,538 × 83,538
4. Step 4: Simplify right side
   53,820x = 6,978,597,444
5. Step 5: Solve for x
   x = 6,978,597,444/53,820
6. Step 6: Final answer
   x = 129,665.50