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Finding the Third Proportional to 13,709 and 19,411

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Solution

The third proportional to 13,709 and 19,411 is: 27,484.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,709 : 19,411 = 19,411 : x
  2. Step 2: Convert to fraction form
    13,709/19,411 = 19,411/x
  3. Step 3: Cross multiply
    13,709x = 19,411 × 19,411
  4. Step 4: Simplify right side
    13,709x = 376,786,921
  5. Step 5: Solve for x
    x = 376,786,921/13,709
  6. Step 6: Final answer
    x = 27,484.64

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.