Finding the Third Proportional to 1,006 and 1,686.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,006 : 1,686.50 = 1,686.50 : x
2. Step 2: Convert to fraction form
   1,006/1,686.50 = 1,686.50/x
3. Step 3: Cross multiply
   1,006x = 1,686.50 × 1,686.50
4. Step 4: Simplify right side
   1,006x = 2,844,282.25
5. Step 5: Solve for x
   x = 2,844,282.25/1,006
6. Step 6: Final answer
   x = 2,827.32