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Finding the Third Proportional to 6,414 and 9,471

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Solution

The third proportional to 6,414 and 9,471 is: 13,985.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,414 : 9,471 = 9,471 : x
  2. Step 2: Convert to fraction form
    6,414/9,471 = 9,471/x
  3. Step 3: Cross multiply
    6,414x = 9,471 × 9,471
  4. Step 4: Simplify right side
    6,414x = 89,699,841
  5. Step 5: Solve for x
    x = 89,699,841/6,414
  6. Step 6: Final answer
    x = 13,985.01

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.