Finding the Third Proportional to 735 and 1,178.50

Step by Step Solution

1. Step 1: Write the proportion equation
   735 : 1,178.50 = 1,178.50 : x
2. Step 2: Convert to fraction form
   735/1,178.50 = 1,178.50/x
3. Step 3: Cross multiply
   735x = 1,178.50 × 1,178.50
4. Step 4: Simplify right side
   735x = 1,388,862.25
5. Step 5: Solve for x
   x = 1,388,862.25/735
6. Step 6: Final answer
   x = 1,889.61