Finding the Third Proportional to 781 and 1,746.50

Step by Step Solution

1. Step 1: Write the proportion equation
   781 : 1,746.50 = 1,746.50 : x
2. Step 2: Convert to fraction form
   781/1,746.50 = 1,746.50/x
3. Step 3: Cross multiply
   781x = 1,746.50 × 1,746.50
4. Step 4: Simplify right side
   781x = 3,050,262.25
5. Step 5: Solve for x
   x = 3,050,262.25/781
6. Step 6: Final answer
   x = 3,905.59