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Finding the Third Proportional to 8,412 and 18,031

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Solution

The third proportional to 8,412 and 18,031 is: 38,649.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,412 : 18,031 = 18,031 : x
  2. Step 2: Convert to fraction form
    8,412/18,031 = 18,031/x
  3. Step 3: Cross multiply
    8,412x = 18,031 × 18,031
  4. Step 4: Simplify right side
    8,412x = 325,116,961
  5. Step 5: Solve for x
    x = 325,116,961/8,412
  6. Step 6: Final answer
    x = 38,649.19

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.