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Finding the Third Proportional to 6,508 and 13,424

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Solution

The third proportional to 6,508 and 13,424 is: 27,689.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,508 : 13,424 = 13,424 : x
  2. Step 2: Convert to fraction form
    6,508/13,424 = 13,424/x
  3. Step 3: Cross multiply
    6,508x = 13,424 × 13,424
  4. Step 4: Simplify right side
    6,508x = 180,203,776
  5. Step 5: Solve for x
    x = 180,203,776/6,508
  6. Step 6: Final answer
    x = 27,689.58

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.