Finding the Third Proportional to 1,003 and 1,686

Step by Step Solution

1. Step 1: Write the proportion equation
   1,003 : 1,686 = 1,686 : x
2. Step 2: Convert to fraction form
   1,003/1,686 = 1,686/x
3. Step 3: Cross multiply
   1,003x = 1,686 × 1,686
4. Step 4: Simplify right side
   1,003x = 2,842,596
5. Step 5: Solve for x
   x = 2,842,596/1,003
6. Step 6: Final answer
   x = 2,834.09