Finding the Third Proportional to 729 and 1,072.50

Step by Step Solution

1. Step 1: Write the proportion equation
   729 : 1,072.50 = 1,072.50 : x
2. Step 2: Convert to fraction form
   729/1,072.50 = 1,072.50/x
3. Step 3: Cross multiply
   729x = 1,072.50 × 1,072.50
4. Step 4: Simplify right side
   729x = 1,150,256.25
5. Step 5: Solve for x
   x = 1,150,256.25/729
6. Step 6: Final answer
   x = 1,577.85