Finding the Third Proportional to 37,461 and 81,823.50

Step by Step Solution

1. Step 1: Write the proportion equation
   37,461 : 81,823.50 = 81,823.50 : x
2. Step 2: Convert to fraction form
   37,461/81,823.50 = 81,823.50/x
3. Step 3: Cross multiply
   37,461x = 81,823.50 × 81,823.50
4. Step 4: Simplify right side
   37,461x = 6,695,085,152.25
5. Step 5: Solve for x
   x = 6,695,085,152.25/37,461
6. Step 6: Final answer
   x = 178,721.47