Finding the Third Proportional to 772.50 and 1,665

Step by Step Solution

1. Step 1: Write the proportion equation
   772.50 : 1,665 = 1,665 : x
2. Step 2: Convert to fraction form
   772.50/1,665 = 1,665/x
3. Step 3: Cross multiply
   772.50x = 1,665 × 1,665
4. Step 4: Simplify right side
   772.50x = 2,772,225
5. Step 5: Solve for x
   x = 2,772,225/772.50
6. Step 6: Final answer
   x = 3,588.64