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Finding the Third Proportional to 6,514 and 12,702

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Solution

The third proportional to 6,514 and 12,702 is: 24,768.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,514 : 12,702 = 12,702 : x
  2. Step 2: Convert to fraction form
    6,514/12,702 = 12,702/x
  3. Step 3: Cross multiply
    6,514x = 12,702 × 12,702
  4. Step 4: Simplify right side
    6,514x = 161,340,804
  5. Step 5: Solve for x
    x = 161,340,804/6,514
  6. Step 6: Final answer
    x = 24,768.32

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.