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Finding the Third Proportional to 20,717 and 31,970

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Solution

The third proportional to 20,717 and 31,970 is: 49,335.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,717 : 31,970 = 31,970 : x
  2. Step 2: Convert to fraction form
    20,717/31,970 = 31,970/x
  3. Step 3: Cross multiply
    20,717x = 31,970 × 31,970
  4. Step 4: Simplify right side
    20,717x = 1,022,080,900
  5. Step 5: Solve for x
    x = 1,022,080,900/20,717
  6. Step 6: Final answer
    x = 49,335.37

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.