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Finding the Third Proportional to 20,438 and 31,657

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Solution

The third proportional to 20,438 and 31,657 is: 49,034.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,438 : 31,657 = 31,657 : x
  2. Step 2: Convert to fraction form
    20,438/31,657 = 31,657/x
  3. Step 3: Cross multiply
    20,438x = 31,657 × 31,657
  4. Step 4: Simplify right side
    20,438x = 1,002,165,649
  5. Step 5: Solve for x
    x = 1,002,165,649/20,438
  6. Step 6: Final answer
    x = 49,034.43

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.