Finding the Third Proportional to 1,586.50 and 2,401.75

Step by Step Solution

1. Step 1: Write the proportion equation
   1,586.50 : 2,401.75 = 2,401.75 : x
2. Step 2: Convert to fraction form
   1,586.50/2,401.75 = 2,401.75/x
3. Step 3: Cross multiply
   1,586.50x = 2,401.75 × 2,401.75
4. Step 4: Simplify right side
   1,586.50x = 5,768,403.06
5. Step 5: Solve for x
   x = 5,768,403.06/1,586.50
6. Step 6: Final answer
   x = 3,635.93