Finding the Third Proportional to 527.50 and 827.50

Step by Step Solution

1. Step 1: Write the proportion equation
   527.50 : 827.50 = 827.50 : x
2. Step 2: Convert to fraction form
   527.50/827.50 = 827.50/x
3. Step 3: Cross multiply
   527.50x = 827.50 × 827.50
4. Step 4: Simplify right side
   527.50x = 684,756.25
5. Step 5: Solve for x
   x = 684,756.25/527.50
6. Step 6: Final answer
   x = 1,298.12