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Finding the Third Proportional to 13,999 and 21,709

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Solution

The third proportional to 13,999 and 21,709 is: 33,665.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,999 : 21,709 = 21,709 : x
  2. Step 2: Convert to fraction form
    13,999/21,709 = 21,709/x
  3. Step 3: Cross multiply
    13,999x = 21,709 × 21,709
  4. Step 4: Simplify right side
    13,999x = 471,280,681
  5. Step 5: Solve for x
    x = 471,280,681/13,999
  6. Step 6: Final answer
    x = 33,665.31

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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.