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Finding the Third Proportional to 20,438 and 31,577

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Solution

The third proportional to 20,438 and 31,577 is: 48,786.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,438 : 31,577 = 31,577 : x
  2. Step 2: Convert to fraction form
    20,438/31,577 = 31,577/x
  3. Step 3: Cross multiply
    20,438x = 31,577 × 31,577
  4. Step 4: Simplify right side
    20,438x = 997,106,929
  5. Step 5: Solve for x
    x = 997,106,929/20,438
  6. Step 6: Final answer
    x = 48,786.91

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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.