Finding the Third Proportional to 6,414.75 and 7,006.50

Step by Step Solution

1. Step 1: Write the proportion equation
   6,414.75 : 7,006.50 = 7,006.50 : x
2. Step 2: Convert to fraction form
   6,414.75/7,006.50 = 7,006.50/x
3. Step 3: Cross multiply
   6,414.75x = 7,006.50 × 7,006.50
4. Step 4: Simplify right side
   6,414.75x = 49,091,042.25
5. Step 5: Solve for x
   x = 49,091,042.25/6,414.75
6. Step 6: Final answer
   x = 7,652.84