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Finding the Third Proportional to 9,769 and 14,471

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Solution

The third proportional to 9,769 and 14,471 is: 21,436.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,769 : 14,471 = 14,471 : x
  2. Step 2: Convert to fraction form
    9,769/14,471 = 14,471/x
  3. Step 3: Cross multiply
    9,769x = 14,471 × 14,471
  4. Step 4: Simplify right side
    9,769x = 209,409,841
  5. Step 5: Solve for x
    x = 209,409,841/9,769
  6. Step 6: Final answer
    x = 21,436.16

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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.