Finding the Third Proportional to 19,683 and 42,646.50

Step by Step Solution

1. Step 1: Write the proportion equation
   19,683 : 42,646.50 = 42,646.50 : x
2. Step 2: Convert to fraction form
   19,683/42,646.50 = 42,646.50/x
3. Step 3: Cross multiply
   19,683x = 42,646.50 × 42,646.50
4. Step 4: Simplify right side
   19,683x = 1,818,723,962.25
5. Step 5: Solve for x
   x = 1,818,723,962.25/19,683
6. Step 6: Final answer
   x = 92,400.75