Finding the Third Proportional to 37,746 and 83,538

Step by Step Solution

1. Step 1: Write the proportion equation
   37,746 : 83,538 = 83,538 : x
2. Step 2: Convert to fraction form
   37,746/83,538 = 83,538/x
3. Step 3: Cross multiply
   37,746x = 83,538 × 83,538
4. Step 4: Simplify right side
   37,746x = 6,978,597,444
5. Step 5: Solve for x
   x = 6,978,597,444/37,746
6. Step 6: Final answer
   x = 184,883.10