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Finding the Third Proportional to 5,877 and 6,453

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Solution

The third proportional to 5,877 and 6,453 is: 7,085.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,877 : 6,453 = 6,453 : x
  2. Step 2: Convert to fraction form
    5,877/6,453 = 6,453/x
  3. Step 3: Cross multiply
    5,877x = 6,453 × 6,453
  4. Step 4: Simplify right side
    5,877x = 41,641,209
  5. Step 5: Solve for x
    x = 41,641,209/5,877
  6. Step 6: Final answer
    x = 7,085.45

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.