Finding the Third Proportional to 822.56 and 975.56

Step by Step Solution

1. Step 1: Write the proportion equation
   822.56 : 975.56 = 975.56 : x
2. Step 2: Convert to fraction form
   822.56/975.56 = 975.56/x
3. Step 3: Cross multiply
   822.56x = 975.56 × 975.56
4. Step 4: Simplify right side
   822.56x = 951,722.19
5. Step 5: Solve for x
   x = 951,722.19/822.56
6. Step 6: Final answer
   x = 1,157.02