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Finding the Third Proportional to 6,419 and 9,407

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Solution

The third proportional to 6,419 and 9,407 is: 13,785.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,419 : 9,407 = 9,407 : x
  2. Step 2: Convert to fraction form
    6,419/9,407 = 9,407/x
  3. Step 3: Cross multiply
    6,419x = 9,407 × 9,407
  4. Step 4: Simplify right side
    6,419x = 88,491,649
  5. Step 5: Solve for x
    x = 88,491,649/6,419
  6. Step 6: Final answer
    x = 13,785.89

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.