Finding the Third Proportional to 586.50 and 687.50

Step by Step Solution

1. Step 1: Write the proportion equation
   586.50 : 687.50 = 687.50 : x
2. Step 2: Convert to fraction form
   586.50/687.50 = 687.50/x
3. Step 3: Cross multiply
   586.50x = 687.50 × 687.50
4. Step 4: Simplify right side
   586.50x = 472,656.25
5. Step 5: Solve for x
   x = 472,656.25/586.50
6. Step 6: Final answer
   x = 805.89