Finding the Third Proportional to 678 and 1,477.50

Step by Step Solution

1. Step 1: Write the proportion equation
   678 : 1,477.50 = 1,477.50 : x
2. Step 2: Convert to fraction form
   678/1,477.50 = 1,477.50/x
3. Step 3: Cross multiply
   678x = 1,477.50 × 1,477.50
4. Step 4: Simplify right side
   678x = 2,183,006.25
5. Step 5: Solve for x
   x = 2,183,006.25/678
6. Step 6: Final answer
   x = 3,219.77