Finding the Third Proportional to 37,977.75 and 83,106.75

Step by Step Solution

1. Step 1: Write the proportion equation
   37,977.75 : 83,106.75 = 83,106.75 : x
2. Step 2: Convert to fraction form
   37,977.75/83,106.75 = 83,106.75/x
3. Step 3: Cross multiply
   37,977.75x = 83,106.75 × 83,106.75
4. Step 4: Simplify right side
   37,977.75x = 6,906,731,895.56
5. Step 5: Solve for x
   x = 6,906,731,895.56/37,977.75
6. Step 6: Final answer
   x = 181,862.59