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Finding the Third Proportional to 5,782 and 9,497

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Solution

The third proportional to 5,782 and 9,497 is: 15,598.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,782 : 9,497 = 9,497 : x
  2. Step 2: Convert to fraction form
    5,782/9,497 = 9,497/x
  3. Step 3: Cross multiply
    5,782x = 9,497 × 9,497
  4. Step 4: Simplify right side
    5,782x = 90,193,009
  5. Step 5: Solve for x
    x = 90,193,009/5,782
  6. Step 6: Final answer
    x = 15,598.93

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.