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Finding the Third Proportional to 6,406 and 8,089

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Solution

The third proportional to 6,406 and 8,089 is: 10,214.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,406 : 8,089 = 8,089 : x
  2. Step 2: Convert to fraction form
    6,406/8,089 = 8,089/x
  3. Step 3: Cross multiply
    6,406x = 8,089 × 8,089
  4. Step 4: Simplify right side
    6,406x = 65,431,921
  5. Step 5: Solve for x
    x = 65,431,921/6,406
  6. Step 6: Final answer
    x = 10,214.16

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.