Finding the Third Proportional to 2,564 and 4,162

Step by Step Solution

1. Step 1: Write the proportion equation
   2,564 : 4,162 = 4,162 : x
2. Step 2: Convert to fraction form
   2,564/4,162 = 4,162/x
3. Step 3: Cross multiply
   2,564x = 4,162 × 4,162
4. Step 4: Simplify right side
   2,564x = 17,322,244
5. Step 5: Solve for x
   x = 17,322,244/2,564
6. Step 6: Final answer
   x = 6,755.95