Finding the Third Proportional to 277.59 and 586.83

Step by Step Solution

1. Step 1: Write the proportion equation
   277.59 : 586.83 = 586.83 : x
2. Step 2: Convert to fraction form
   277.59/586.83 = 586.83/x
3. Step 3: Cross multiply
   277.59x = 586.83 × 586.83
4. Step 4: Simplify right side
   277.59x = 344,367.25
5. Step 5: Solve for x
   x = 344,367.25/277.59
6. Step 6: Final answer
   x = 1,240.54