Finding the Third Proportional to 37,802 and 82,406

Step by Step Solution

1. Step 1: Write the proportion equation
   37,802 : 82,406 = 82,406 : x
2. Step 2: Convert to fraction form
   37,802/82,406 = 82,406/x
3. Step 3: Cross multiply
   37,802x = 82,406 × 82,406
4. Step 4: Simplify right side
   37,802x = 6,790,748,836
5. Step 5: Solve for x
   x = 6,790,748,836/37,802
6. Step 6: Final answer
   x = 179,639.94