Finding the Third Proportional to 1,016 and 1,584

Step by Step Solution

1. Step 1: Write the proportion equation
   1,016 : 1,584 = 1,584 : x
2. Step 2: Convert to fraction form
   1,016/1,584 = 1,584/x
3. Step 3: Cross multiply
   1,016x = 1,584 × 1,584
4. Step 4: Simplify right side
   1,016x = 2,509,056
5. Step 5: Solve for x
   x = 2,509,056/1,016
6. Step 6: Final answer
   x = 2,469.54