Finding the Third Proportional to 106 and 280.50

Step by Step Solution

1. Step 1: Write the proportion equation
   106 : 280.50 = 280.50 : x
2. Step 2: Convert to fraction form
   106/280.50 = 280.50/x
3. Step 3: Cross multiply
   106x = 280.50 × 280.50
4. Step 4: Simplify right side
   106x = 78,680.25
5. Step 5: Solve for x
   x = 78,680.25/106
6. Step 6: Final answer
   x = 742.27