Finding the Third Proportional to 522.50 and 782.50

Step by Step Solution

1. Step 1: Write the proportion equation
   522.50 : 782.50 = 782.50 : x
2. Step 2: Convert to fraction form
   522.50/782.50 = 782.50/x
3. Step 3: Cross multiply
   522.50x = 782.50 × 782.50
4. Step 4: Simplify right side
   522.50x = 612,306.25
5. Step 5: Solve for x
   x = 612,306.25/522.50
6. Step 6: Final answer
   x = 1,171.88