Finding the Third Proportional to 1,584.56 and 2,414.81

Step by Step Solution

1. Step 1: Write the proportion equation
   1,584.56 : 2,414.81 = 2,414.81 : x
2. Step 2: Convert to fraction form
   1,584.56/2,414.81 = 2,414.81/x
3. Step 3: Cross multiply
   1,584.56x = 2,414.81 × 2,414.81
4. Step 4: Simplify right side
   1,584.56x = 5,831,319.41
5. Step 5: Solve for x
   x = 5,831,319.41/1,584.56
6. Step 6: Final answer
   x = 3,680.08