Finding the Third Proportional to 37,648 and 81,780

Step by Step Solution

1. Step 1: Write the proportion equation
   37,648 : 81,780 = 81,780 : x
2. Step 2: Convert to fraction form
   37,648/81,780 = 81,780/x
3. Step 3: Cross multiply
   37,648x = 81,780 × 81,780
4. Step 4: Simplify right side
   37,648x = 6,687,968,400
5. Step 5: Solve for x
   x = 6,687,968,400/37,648
6. Step 6: Final answer
   x = 177,644.72