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Finding the Third Proportional to 5,971 and 7,857

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Solution

The third proportional to 5,971 and 7,857 is: 10,338.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,971 : 7,857 = 7,857 : x
  2. Step 2: Convert to fraction form
    5,971/7,857 = 7,857/x
  3. Step 3: Cross multiply
    5,971x = 7,857 × 7,857
  4. Step 4: Simplify right side
    5,971x = 61,732,449
  5. Step 5: Solve for x
    x = 61,732,449/5,971
  6. Step 6: Final answer
    x = 10,338.71

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.