Finding the Third Proportional to 582.50 and 830.50

Step by Step Solution

1. Step 1: Write the proportion equation
   582.50 : 830.50 = 830.50 : x
2. Step 2: Convert to fraction form
   582.50/830.50 = 830.50/x
3. Step 3: Cross multiply
   582.50x = 830.50 × 830.50
4. Step 4: Simplify right side
   582.50x = 689,730.25
5. Step 5: Solve for x
   x = 689,730.25/582.50
6. Step 6: Final answer
   x = 1,184.09