Finding the Third Proportional to 2,584.13 and 5,637.38

Step by Step Solution

1. Step 1: Write the proportion equation
   2,584.13 : 5,637.38 = 5,637.38 : x
2. Step 2: Convert to fraction form
   2,584.13/5,637.38 = 5,637.38/x
3. Step 3: Cross multiply
   2,584.13x = 5,637.38 × 5,637.38
4. Step 4: Simplify right side
   2,584.13x = 31,779,996.89
5. Step 5: Solve for x
   x = 31,779,996.89/2,584.13
6. Step 6: Final answer
   x = 12,298.17