Finding the Third Proportional to 826 and 1,306.50

Step by Step Solution

1. Step 1: Write the proportion equation
   826 : 1,306.50 = 1,306.50 : x
2. Step 2: Convert to fraction form
   826/1,306.50 = 1,306.50/x
3. Step 3: Cross multiply
   826x = 1,306.50 × 1,306.50
4. Step 4: Simplify right side
   826x = 1,706,942.25
5. Step 5: Solve for x
   x = 1,706,942.25/826
6. Step 6: Final answer
   x = 2,066.52