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Finding the Third Proportional to 10,971 and 24,031

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Solution

The third proportional to 10,971 and 24,031 is: 52,637.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,971 : 24,031 = 24,031 : x
  2. Step 2: Convert to fraction form
    10,971/24,031 = 24,031/x
  3. Step 3: Cross multiply
    10,971x = 24,031 × 24,031
  4. Step 4: Simplify right side
    10,971x = 577,488,961
  5. Step 5: Solve for x
    x = 577,488,961/10,971
  6. Step 6: Final answer
    x = 52,637.77

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.