Finding the Third Proportional to 2,378 and 5,654

Step by Step Solution

1. Step 1: Write the proportion equation
   2,378 : 5,654 = 5,654 : x
2. Step 2: Convert to fraction form
   2,378/5,654 = 5,654/x
3. Step 3: Cross multiply
   2,378x = 5,654 × 5,654
4. Step 4: Simplify right side
   2,378x = 31,967,716
5. Step 5: Solve for x
   x = 31,967,716/2,378
6. Step 6: Final answer
   x = 13,443.11