Finding the Third Proportional to 37,829 and 82,091

Step by Step Solution

1. Step 1: Write the proportion equation
   37,829 : 82,091 = 82,091 : x
2. Step 2: Convert to fraction form
   37,829/82,091 = 82,091/x
3. Step 3: Cross multiply
   37,829x = 82,091 × 82,091
4. Step 4: Simplify right side
   37,829x = 6,738,932,281
5. Step 5: Solve for x
   x = 6,738,932,281/37,829
6. Step 6: Final answer
   x = 178,141.96