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Finding the Third Proportional to 65,727 and 102,971

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Solution

The third proportional to 65,727 and 102,971 is: 161,319.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,727 : 102,971 = 102,971 : x
  2. Step 2: Convert to fraction form
    65,727/102,971 = 102,971/x
  3. Step 3: Cross multiply
    65,727x = 102,971 × 102,971
  4. Step 4: Simplify right side
    65,727x = 10,603,026,841
  5. Step 5: Solve for x
    x = 10,603,026,841/65,727
  6. Step 6: Final answer
    x = 161,319.20

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.