Finding the Third Proportional to 37,688 and 81,856

Step by Step Solution

1. Step 1: Write the proportion equation
   37,688 : 81,856 = 81,856 : x
2. Step 2: Convert to fraction form
   37,688/81,856 = 81,856/x
3. Step 3: Cross multiply
   37,688x = 81,856 × 81,856
4. Step 4: Simplify right side
   37,688x = 6,700,404,736
5. Step 5: Solve for x
   x = 6,700,404,736/37,688
6. Step 6: Final answer
   x = 177,786.16