Finding the Third Proportional to 102 and 162.50

Step by Step Solution

1. Step 1: Write the proportion equation
   102 : 162.50 = 162.50 : x
2. Step 2: Convert to fraction form
   102/162.50 = 162.50/x
3. Step 3: Cross multiply
   102x = 162.50 × 162.50
4. Step 4: Simplify right side
   102x = 26,406.25
5. Step 5: Solve for x
   x = 26,406.25/102
6. Step 6: Final answer
   x = 258.88