Finding the Third Proportional to 642.50 and 705.50

Step by Step Solution

1. Step 1: Write the proportion equation
   642.50 : 705.50 = 705.50 : x
2. Step 2: Convert to fraction form
   642.50/705.50 = 705.50/x
3. Step 3: Cross multiply
   642.50x = 705.50 × 705.50
4. Step 4: Simplify right side
   642.50x = 497,730.25
5. Step 5: Solve for x
   x = 497,730.25/642.50
6. Step 6: Final answer
   x = 774.68