Finding the Third Proportional to 37,666 and 83,593

Step by Step Solution

1. Step 1: Write the proportion equation
   37,666 : 83,593 = 83,593 : x
2. Step 2: Convert to fraction form
   37,666/83,593 = 83,593/x
3. Step 3: Cross multiply
   37,666x = 83,593 × 83,593
4. Step 4: Simplify right side
   37,666x = 6,987,789,649
5. Step 5: Solve for x
   x = 6,987,789,649/37,666
6. Step 6: Final answer
   x = 185,519.82