Finding the Third Proportional to 822 and 1,165.50

Step by Step Solution

1. Step 1: Write the proportion equation
   822 : 1,165.50 = 1,165.50 : x
2. Step 2: Convert to fraction form
   822/1,165.50 = 1,165.50/x
3. Step 3: Cross multiply
   822x = 1,165.50 × 1,165.50
4. Step 4: Simplify right side
   822x = 1,358,390.25
5. Step 5: Solve for x
   x = 1,358,390.25/822
6. Step 6: Final answer
   x = 1,652.54