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Finding the Third Proportional to 19,743 and 31,257

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Solution

The third proportional to 19,743 and 31,257 is: 49,485.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,743 : 31,257 = 31,257 : x
  2. Step 2: Convert to fraction form
    19,743/31,257 = 31,257/x
  3. Step 3: Cross multiply
    19,743x = 31,257 × 31,257
  4. Step 4: Simplify right side
    19,743x = 977,000,049
  5. Step 5: Solve for x
    x = 977,000,049/19,743
  6. Step 6: Final answer
    x = 49,485.90

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.