Finding the Third Proportional to 233 and 546.50

Step by Step Solution

1. Step 1: Write the proportion equation
   233 : 546.50 = 546.50 : x
2. Step 2: Convert to fraction form
   233/546.50 = 546.50/x
3. Step 3: Cross multiply
   233x = 546.50 × 546.50
4. Step 4: Simplify right side
   233x = 298,662.25
5. Step 5: Solve for x
   x = 298,662.25/233
6. Step 6: Final answer
   x = 1,281.81