Finding the Third Proportional to 1,004 and 1,684

Step by Step Solution

1. Step 1: Write the proportion equation
   1,004 : 1,684 = 1,684 : x
2. Step 2: Convert to fraction form
   1,004/1,684 = 1,684/x
3. Step 3: Cross multiply
   1,004x = 1,684 × 1,684
4. Step 4: Simplify right side
   1,004x = 2,835,856
5. Step 5: Solve for x
   x = 2,835,856/1,004
6. Step 6: Final answer
   x = 2,824.56