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Finding the Third Proportional to 5,297 and 6,413

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Solution

The third proportional to 5,297 and 6,413 is: 7,764.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,297 : 6,413 = 6,413 : x
  2. Step 2: Convert to fraction form
    5,297/6,413 = 6,413/x
  3. Step 3: Cross multiply
    5,297x = 6,413 × 6,413
  4. Step 4: Simplify right side
    5,297x = 41,126,569
  5. Step 5: Solve for x
    x = 41,126,569/5,297
  6. Step 6: Final answer
    x = 7,764.12

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.