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Finding the Third Proportional to 6,404 and 7,876

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Solution

The third proportional to 6,404 and 7,876 is: 9,686.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,404 : 7,876 = 7,876 : x
  2. Step 2: Convert to fraction form
    6,404/7,876 = 7,876/x
  3. Step 3: Cross multiply
    6,404x = 7,876 × 7,876
  4. Step 4: Simplify right side
    6,404x = 62,031,376
  5. Step 5: Solve for x
    x = 62,031,376/6,404
  6. Step 6: Final answer
    x = 9,686.35

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Why These Related Problems?

These problems maintain the same ratio (1.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.