Finding the Third Proportional to 37,872 and 78,205.50

Step by Step Solution

1. Step 1: Write the proportion equation
   37,872 : 78,205.50 = 78,205.50 : x
2. Step 2: Convert to fraction form
   37,872/78,205.50 = 78,205.50/x
3. Step 3: Cross multiply
   37,872x = 78,205.50 × 78,205.50
4. Step 4: Simplify right side
   37,872x = 6,116,100,230.25
5. Step 5: Solve for x
   x = 6,116,100,230.25/37,872
6. Step 6: Final answer
   x = 161,493.99