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Finding the Third Proportional to 6,514 and 13,682

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Solution

The third proportional to 6,514 and 13,682 is: 28,737.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,514 : 13,682 = 13,682 : x
  2. Step 2: Convert to fraction form
    6,514/13,682 = 13,682/x
  3. Step 3: Cross multiply
    6,514x = 13,682 × 13,682
  4. Step 4: Simplify right side
    6,514x = 187,197,124
  5. Step 5: Solve for x
    x = 187,197,124/6,514
  6. Step 6: Final answer
    x = 28,737.66

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.