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Finding the Third Proportional to 4,102 and 9,877

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Solution

The third proportional to 4,102 and 9,877 is: 23,782.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,102 : 9,877 = 9,877 : x
  2. Step 2: Convert to fraction form
    4,102/9,877 = 9,877/x
  3. Step 3: Cross multiply
    4,102x = 9,877 × 9,877
  4. Step 4: Simplify right side
    4,102x = 97,555,129
  5. Step 5: Solve for x
    x = 97,555,129/4,102
  6. Step 6: Final answer
    x = 23,782.33

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.