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Finding the Third Proportional to 20,965 and 31,717

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Solution

The third proportional to 20,965 and 31,717 is: 47,983.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,965 : 31,717 = 31,717 : x
  2. Step 2: Convert to fraction form
    20,965/31,717 = 31,717/x
  3. Step 3: Cross multiply
    20,965x = 31,717 × 31,717
  4. Step 4: Simplify right side
    20,965x = 1,005,968,089
  5. Step 5: Solve for x
    x = 1,005,968,089/20,965
  6. Step 6: Final answer
    x = 47,983.21

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.