Finding the Third Proportional to 37,806 and 82,172

Step by Step Solution

1. Step 1: Write the proportion equation
   37,806 : 82,172 = 82,172 : x
2. Step 2: Convert to fraction form
   37,806/82,172 = 82,172/x
3. Step 3: Cross multiply
   37,806x = 82,172 × 82,172
4. Step 4: Simplify right side
   37,806x = 6,752,237,584
5. Step 5: Solve for x
   x = 6,752,237,584/37,806
6. Step 6: Final answer
   x = 178,602.27