Finding the Third Proportional to 456 and 688.50

Step by Step Solution

1. Step 1: Write the proportion equation
   456 : 688.50 = 688.50 : x
2. Step 2: Convert to fraction form
   456/688.50 = 688.50/x
3. Step 3: Cross multiply
   456x = 688.50 × 688.50
4. Step 4: Simplify right side
   456x = 474,032.25
5. Step 5: Solve for x
   x = 474,032.25/456
6. Step 6: Final answer
   x = 1,039.54