Finding the Third Proportional to 1,296 and 1,822.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,296 : 1,822.50 = 1,822.50 : x
2. Step 2: Convert to fraction form
   1,296/1,822.50 = 1,822.50/x
3. Step 3: Cross multiply
   1,296x = 1,822.50 × 1,822.50
4. Step 4: Simplify right side
   1,296x = 3,321,506.25
5. Step 5: Solve for x
   x = 3,321,506.25/1,296
6. Step 6: Final answer
   x = 2,562.89