Finding the Third Proportional to 37,686 and 82,770

Step by Step Solution

1. Step 1: Write the proportion equation
   37,686 : 82,770 = 82,770 : x
2. Step 2: Convert to fraction form
   37,686/82,770 = 82,770/x
3. Step 3: Cross multiply
   37,686x = 82,770 × 82,770
4. Step 4: Simplify right side
   37,686x = 6,850,872,900
5. Step 5: Solve for x
   x = 6,850,872,900/37,686
6. Step 6: Final answer
   x = 181,788.27