Finding the Third Proportional to 123.16 and 185.10

Step by Step Solution

1. Step 1: Write the proportion equation
   123.16 : 185.10 = 185.10 : x
2. Step 2: Convert to fraction form
   123.16/185.10 = 185.10/x
3. Step 3: Cross multiply
   123.16x = 185.10 × 185.10
4. Step 4: Simplify right side
   123.16x = 34,261.14
5. Step 5: Solve for x
   x = 34,261.14/123.16
6. Step 6: Final answer
   x = 278.18