Finding the Third Proportional to 727.50 and 784.50

Step by Step Solution

1. Step 1: Write the proportion equation
   727.50 : 784.50 = 784.50 : x
2. Step 2: Convert to fraction form
   727.50/784.50 = 784.50/x
3. Step 3: Cross multiply
   727.50x = 784.50 × 784.50
4. Step 4: Simplify right side
   727.50x = 615,440.25
5. Step 5: Solve for x
   x = 615,440.25/727.50
6. Step 6: Final answer
   x = 845.97