Finding the Third Proportional to 827 and 1,308.50

Step by Step Solution

1. Step 1: Write the proportion equation
   827 : 1,308.50 = 1,308.50 : x
2. Step 2: Convert to fraction form
   827/1,308.50 = 1,308.50/x
3. Step 3: Cross multiply
   827x = 1,308.50 × 1,308.50
4. Step 4: Simplify right side
   827x = 1,712,172.25
5. Step 5: Solve for x
   x = 1,712,172.25/827
6. Step 6: Final answer
   x = 2,070.34