Finding the Third Proportional to 123.50 and 180.25

Step by Step Solution

1. Step 1: Write the proportion equation
   123.50 : 180.25 = 180.25 : x
2. Step 2: Convert to fraction form
   123.50/180.25 = 180.25/x
3. Step 3: Cross multiply
   123.50x = 180.25 × 180.25
4. Step 4: Simplify right side
   123.50x = 32,490.06
5. Step 5: Solve for x
   x = 32,490.06/123.50
6. Step 6: Final answer
   x = 263.08