Finding the Third Proportional to 37,665 and 83,590.50

Step by Step Solution

1. Step 1: Write the proportion equation
   37,665 : 83,590.50 = 83,590.50 : x
2. Step 2: Convert to fraction form
   37,665/83,590.50 = 83,590.50/x
3. Step 3: Cross multiply
   37,665x = 83,590.50 × 83,590.50
4. Step 4: Simplify right side
   37,665x = 6,987,371,690.25
5. Step 5: Solve for x
   x = 6,987,371,690.25/37,665
6. Step 6: Final answer
   x = 185,513.65