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Finding the Third Proportional to 20,498 and 31,840

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Solution

The third proportional to 20,498 and 31,840 is: 49,457.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,498 : 31,840 = 31,840 : x
  2. Step 2: Convert to fraction form
    20,498/31,840 = 31,840/x
  3. Step 3: Cross multiply
    20,498x = 31,840 × 31,840
  4. Step 4: Simplify right side
    20,498x = 1,013,785,600
  5. Step 5: Solve for x
    x = 1,013,785,600/20,498
  6. Step 6: Final answer
    x = 49,457.78

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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.