Finding the Third Proportional to 822 and 2,137.50

Step by Step Solution

1. Step 1: Write the proportion equation
   822 : 2,137.50 = 2,137.50 : x
2. Step 2: Convert to fraction form
   822/2,137.50 = 2,137.50/x
3. Step 3: Cross multiply
   822x = 2,137.50 × 2,137.50
4. Step 4: Simplify right side
   822x = 4,568,906.25
5. Step 5: Solve for x
   x = 4,568,906.25/822
6. Step 6: Final answer
   x = 5,558.28