Finding the Third Proportional to 409 and 1,103.50

Step by Step Solution

1. Step 1: Write the proportion equation
   409 : 1,103.50 = 1,103.50 : x
2. Step 2: Convert to fraction form
   409/1,103.50 = 1,103.50/x
3. Step 3: Cross multiply
   409x = 1,103.50 × 1,103.50
4. Step 4: Simplify right side
   409x = 1,217,712.25
5. Step 5: Solve for x
   x = 1,217,712.25/409
6. Step 6: Final answer
   x = 2,977.29