Finding the Third Proportional to 37,977.50 and 83,106.50

Step by Step Solution

1. Step 1: Write the proportion equation
   37,977.50 : 83,106.50 = 83,106.50 : x
2. Step 2: Convert to fraction form
   37,977.50/83,106.50 = 83,106.50/x
3. Step 3: Cross multiply
   37,977.50x = 83,106.50 × 83,106.50
4. Step 4: Simplify right side
   37,977.50x = 6,906,690,342.25
5. Step 5: Solve for x
   x = 6,906,690,342.25/37,977.50
6. Step 6: Final answer
   x = 181,862.69