Finding the Third Proportional to 37,786.50 and 82,377

Step by Step Solution

1. Step 1: Write the proportion equation
   37,786.50 : 82,377 = 82,377 : x
2. Step 2: Convert to fraction form
   37,786.50/82,377 = 82,377/x
3. Step 3: Cross multiply
   37,786.50x = 82,377 × 82,377
4. Step 4: Simplify right side
   37,786.50x = 6,785,970,129
5. Step 5: Solve for x
   x = 6,785,970,129/37,786.50
6. Step 6: Final answer
   x = 179,587.16