Finding the Third Proportional to 781.50 and 1,005

Step by Step Solution

1. Step 1: Write the proportion equation
   781.50 : 1,005 = 1,005 : x
2. Step 2: Convert to fraction form
   781.50/1,005 = 1,005/x
3. Step 3: Cross multiply
   781.50x = 1,005 × 1,005
4. Step 4: Simplify right side
   781.50x = 1,010,025
5. Step 5: Solve for x
   x = 1,010,025/781.50
6. Step 6: Final answer
   x = 1,292.42