Finding the Third Proportional to 37,800 and 82,507.50

Step by Step Solution

1. Step 1: Write the proportion equation
   37,800 : 82,507.50 = 82,507.50 : x
2. Step 2: Convert to fraction form
   37,800/82,507.50 = 82,507.50/x
3. Step 3: Cross multiply
   37,800x = 82,507.50 × 82,507.50
4. Step 4: Simplify right side
   37,800x = 6,807,487,556.25
5. Step 5: Solve for x
   x = 6,807,487,556.25/37,800
6. Step 6: Final answer
   x = 180,092.26