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Finding the Third Proportional to 6,829 and 14,031

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Solution

The third proportional to 6,829 and 14,031 is: 28,828.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,829 : 14,031 = 14,031 : x
  2. Step 2: Convert to fraction form
    6,829/14,031 = 14,031/x
  3. Step 3: Cross multiply
    6,829x = 14,031 × 14,031
  4. Step 4: Simplify right side
    6,829x = 196,868,961
  5. Step 5: Solve for x
    x = 196,868,961/6,829
  6. Step 6: Final answer
    x = 28,828.37

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.