Finding the Third Proportional to 589.78 and 784.55

Step by Step Solution

1. Step 1: Write the proportion equation
   589.78 : 784.55 = 784.55 : x
2. Step 2: Convert to fraction form
   589.78/784.55 = 784.55/x
3. Step 3: Cross multiply
   589.78x = 784.55 × 784.55
4. Step 4: Simplify right side
   589.78x = 615,513.80
5. Step 5: Solve for x
   x = 615,513.80/589.78
6. Step 6: Final answer
   x = 1,043.63