Finding the Third Proportional to 9,585 and 13,770

Step by Step Solution

1. Step 1: Write the proportion equation
   9,585 : 13,770 = 13,770 : x
2. Step 2: Convert to fraction form
   9,585/13,770 = 13,770/x
3. Step 3: Cross multiply
   9,585x = 13,770 × 13,770
4. Step 4: Simplify right side
   9,585x = 189,612,900
5. Step 5: Solve for x
   x = 189,612,900/9,585
6. Step 6: Final answer
   x = 19,782.25