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Finding the Third Proportional to 12,289 and 16,420

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Solution

The third proportional to 12,289 and 16,420 is: 21,939.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,289 : 16,420 = 16,420 : x
  2. Step 2: Convert to fraction form
    12,289/16,420 = 16,420/x
  3. Step 3: Cross multiply
    12,289x = 16,420 × 16,420
  4. Step 4: Simplify right side
    12,289x = 269,616,400
  5. Step 5: Solve for x
    x = 269,616,400/12,289
  6. Step 6: Final answer
    x = 21,939.65

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.