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Finding the Third Proportional to 5,686 and 7,971

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Solution

The third proportional to 5,686 and 7,971 is: 11,174.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,686 : 7,971 = 7,971 : x
  2. Step 2: Convert to fraction form
    5,686/7,971 = 7,971/x
  3. Step 3: Cross multiply
    5,686x = 7,971 × 7,971
  4. Step 4: Simplify right side
    5,686x = 63,536,841
  5. Step 5: Solve for x
    x = 63,536,841/5,686
  6. Step 6: Final answer
    x = 11,174.26

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.