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Finding the Third Proportional to 6,457 and 13,689

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Solution

The third proportional to 6,457 and 13,689 is: 29,021.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,457 : 13,689 = 13,689 : x
  2. Step 2: Convert to fraction form
    6,457/13,689 = 13,689/x
  3. Step 3: Cross multiply
    6,457x = 13,689 × 13,689
  4. Step 4: Simplify right side
    6,457x = 187,388,721
  5. Step 5: Solve for x
    x = 187,388,721/6,457
  6. Step 6: Final answer
    x = 29,021.02

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.