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Finding the Third Proportional to 20,199 and 31,769

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Solution

The third proportional to 20,199 and 31,769 is: 49,966.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,199 : 31,769 = 31,769 : x
  2. Step 2: Convert to fraction form
    20,199/31,769 = 31,769/x
  3. Step 3: Cross multiply
    20,199x = 31,769 × 31,769
  4. Step 4: Simplify right side
    20,199x = 1,009,269,361
  5. Step 5: Solve for x
    x = 1,009,269,361/20,199
  6. Step 6: Final answer
    x = 49,966.30

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.