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Finding the Third Proportional to 4,097 and 6,447

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Solution

The third proportional to 4,097 and 6,447 is: 10,144.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,097 : 6,447 = 6,447 : x
  2. Step 2: Convert to fraction form
    4,097/6,447 = 6,447/x
  3. Step 3: Cross multiply
    4,097x = 6,447 × 6,447
  4. Step 4: Simplify right side
    4,097x = 41,563,809
  5. Step 5: Solve for x
    x = 41,563,809/4,097
  6. Step 6: Final answer
    x = 10,144.94

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.