Finding the Third Proportional to 1,004 and 1,538

Step by Step Solution

1. Step 1: Write the proportion equation
   1,004 : 1,538 = 1,538 : x
2. Step 2: Convert to fraction form
   1,004/1,538 = 1,538/x
3. Step 3: Cross multiply
   1,004x = 1,538 × 1,538
4. Step 4: Simplify right side
   1,004x = 2,365,444
5. Step 5: Solve for x
   x = 2,365,444/1,004
6. Step 6: Final answer
   x = 2,356.02