Finding the Third Proportional to 821 and 1,763.50

Step by Step Solution

1. Step 1: Write the proportion equation
   821 : 1,763.50 = 1,763.50 : x
2. Step 2: Convert to fraction form
   821/1,763.50 = 1,763.50/x
3. Step 3: Cross multiply
   821x = 1,763.50 × 1,763.50
4. Step 4: Simplify right side
   821x = 3,109,932.25
5. Step 5: Solve for x
   x = 3,109,932.25/821
6. Step 6: Final answer
   x = 3,787.98