Finding the Third Proportional to 780 and 2,011.50

Step by Step Solution

1. Step 1: Write the proportion equation
   780 : 2,011.50 = 2,011.50 : x
2. Step 2: Convert to fraction form
   780/2,011.50 = 2,011.50/x
3. Step 3: Cross multiply
   780x = 2,011.50 × 2,011.50
4. Step 4: Simplify right side
   780x = 4,046,132.25
5. Step 5: Solve for x
   x = 4,046,132.25/780
6. Step 6: Final answer
   x = 5,187.35