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Finding the Third Proportional to 5,822 and 8,449

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Solution

The third proportional to 5,822 and 8,449 is: 12,261.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,822 : 8,449 = 8,449 : x
  2. Step 2: Convert to fraction form
    5,822/8,449 = 8,449/x
  3. Step 3: Cross multiply
    5,822x = 8,449 × 8,449
  4. Step 4: Simplify right side
    5,822x = 71,385,601
  5. Step 5: Solve for x
    x = 71,385,601/5,822
  6. Step 6: Final answer
    x = 12,261.35

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.