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Finding the Third Proportional to 4,092 and 9,729

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Solution

The third proportional to 4,092 and 9,729 is: 23,131.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,092 : 9,729 = 9,729 : x
  2. Step 2: Convert to fraction form
    4,092/9,729 = 9,729/x
  3. Step 3: Cross multiply
    4,092x = 9,729 × 9,729
  4. Step 4: Simplify right side
    4,092x = 94,653,441
  5. Step 5: Solve for x
    x = 94,653,441/4,092
  6. Step 6: Final answer
    x = 23,131.34

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.