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Finding the Third Proportional to 19,827 and 31,877

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Solution

The third proportional to 19,827 and 31,877 is: 51,250.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,827 : 31,877 = 31,877 : x
  2. Step 2: Convert to fraction form
    19,827/31,877 = 31,877/x
  3. Step 3: Cross multiply
    19,827x = 31,877 × 31,877
  4. Step 4: Simplify right side
    19,827x = 1,016,143,129
  5. Step 5: Solve for x
    x = 1,016,143,129/19,827
  6. Step 6: Final answer
    x = 51,250.47

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.