Finding the Third Proportional to 582 and 1,266.50

Step by Step Solution

1. Step 1: Write the proportion equation
   582 : 1,266.50 = 1,266.50 : x
2. Step 2: Convert to fraction form
   582/1,266.50 = 1,266.50/x
3. Step 3: Cross multiply
   582x = 1,266.50 × 1,266.50
4. Step 4: Simplify right side
   582x = 1,604,022.25
5. Step 5: Solve for x
   x = 1,604,022.25/582
6. Step 6: Final answer
   x = 2,756.05