Finding the Third Proportional to 1,027.75 and 1,581.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,027.75 : 1,581.50 = 1,581.50 : x
2. Step 2: Convert to fraction form
   1,027.75/1,581.50 = 1,581.50/x
3. Step 3: Cross multiply
   1,027.75x = 1,581.50 × 1,581.50
4. Step 4: Simplify right side
   1,027.75x = 2,501,142.25
5. Step 5: Solve for x
   x = 2,501,142.25/1,027.75
6. Step 6: Final answer
   x = 2,433.61