Finding the Third Proportional to 826.50 and 1,256.25

Step by Step Solution

1. Step 1: Write the proportion equation
   826.50 : 1,256.25 = 1,256.25 : x
2. Step 2: Convert to fraction form
   826.50/1,256.25 = 1,256.25/x
3. Step 3: Cross multiply
   826.50x = 1,256.25 × 1,256.25
4. Step 4: Simplify right side
   826.50x = 1,578,164.06
5. Step 5: Solve for x
   x = 1,578,164.06/826.50
6. Step 6: Final answer
   x = 1,909.45