Finding the Third Proportional to 19,683 and 38,819.25

Step by Step Solution

1. Step 1: Write the proportion equation
   19,683 : 38,819.25 = 38,819.25 : x
2. Step 2: Convert to fraction form
   19,683/38,819.25 = 38,819.25/x
3. Step 3: Cross multiply
   19,683x = 38,819.25 × 38,819.25
4. Step 4: Simplify right side
   19,683x = 1,506,934,170.56
5. Step 5: Solve for x
   x = 1,506,934,170.56/19,683
6. Step 6: Final answer
   x = 76,560.19