Finding the Fourth Proportional to 1,026.29, 1,538.82 and 410.09

Step by Step Solution

1. Step 1: Write the proportion equation
   1,026.29 : 1,538.82 = 410.09 : x
2. Step 2: Convert to fraction form
   1,026.29/1,538.82 = 410.09/x
3. Step 3: Cross multiply
   1,026.29x = 1,538.82 × 410.09
4. Step 4: Simplify right side
   1,026.29x = 631,054.69
5. Step 5: Solve for x
   x = 631,054.69/1,026.29
6. Step 6: Final answer
   x = 614.89