Finding the Third Proportional to 688.50 and 1,584.56

Step by Step Solution

1. Step 1: Write the proportion equation
   688.50 : 1,584.56 = 1,584.56 : x
2. Step 2: Convert to fraction form
   688.50/1,584.56 = 1,584.56/x
3. Step 3: Cross multiply
   688.50x = 1,584.56 × 1,584.56
4. Step 4: Simplify right side
   688.50x = 2,510,838.32
5. Step 5: Solve for x
   x = 2,510,838.32/688.50
6. Step 6: Final answer
   x = 3,646.82