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Finding the Third Proportional to 7,769 and 14,543

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Solution

The third proportional to 7,769 and 14,543 is: 27,223.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,769 : 14,543 = 14,543 : x
  2. Step 2: Convert to fraction form
    7,769/14,543 = 14,543/x
  3. Step 3: Cross multiply
    7,769x = 14,543 × 14,543
  4. Step 4: Simplify right side
    7,769x = 211,498,849
  5. Step 5: Solve for x
    x = 211,498,849/7,769
  6. Step 6: Final answer
    x = 27,223.43

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.