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Finding the Third Proportional to 20,534 and 31,857

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Solution

The third proportional to 20,534 and 31,857 is: 49,423.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,534 : 31,857 = 31,857 : x
  2. Step 2: Convert to fraction form
    20,534/31,857 = 31,857/x
  3. Step 3: Cross multiply
    20,534x = 31,857 × 31,857
  4. Step 4: Simplify right side
    20,534x = 1,014,868,449
  5. Step 5: Solve for x
    x = 1,014,868,449/20,534
  6. Step 6: Final answer
    x = 49,423.81

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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.