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Finding the Third Proportional to 5,732 and 9,102

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Solution

The third proportional to 5,732 and 9,102 is: 14,453.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,732 : 9,102 = 9,102 : x
  2. Step 2: Convert to fraction form
    5,732/9,102 = 9,102/x
  3. Step 3: Cross multiply
    5,732x = 9,102 × 9,102
  4. Step 4: Simplify right side
    5,732x = 82,846,404
  5. Step 5: Solve for x
    x = 82,846,404/5,732
  6. Step 6: Final answer
    x = 14,453.32

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.