Finding the Third Proportional to 37,977 and 83,101.50

Step by Step Solution

1. Step 1: Write the proportion equation
   37,977 : 83,101.50 = 83,101.50 : x
2. Step 2: Convert to fraction form
   37,977/83,101.50 = 83,101.50/x
3. Step 3: Cross multiply
   37,977x = 83,101.50 × 83,101.50
4. Step 4: Simplify right side
   37,977x = 6,905,859,302.25
5. Step 5: Solve for x
   x = 6,905,859,302.25/37,977
6. Step 6: Final answer
   x = 181,843.20