Finding the Third Proportional to 37,880 and 82,596

Step by Step Solution

1. Step 1: Write the proportion equation
   37,880 : 82,596 = 82,596 : x
2. Step 2: Convert to fraction form
   37,880/82,596 = 82,596/x
3. Step 3: Cross multiply
   37,880x = 82,596 × 82,596
4. Step 4: Simplify right side
   37,880x = 6,822,099,216
5. Step 5: Solve for x
   x = 6,822,099,216/37,880
6. Step 6: Final answer
   x = 180,097.66