Finding the Third Proportional to 37,665 and 102,465

Step by Step Solution

1. Step 1: Write the proportion equation
   37,665 : 102,465 = 102,465 : x
2. Step 2: Convert to fraction form
   37,665/102,465 = 102,465/x
3. Step 3: Cross multiply
   37,665x = 102,465 × 102,465
4. Step 4: Simplify right side
   37,665x = 10,499,076,225
5. Step 5: Solve for x
   x = 10,499,076,225/37,665
6. Step 6: Final answer
   x = 278,748.87