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Finding the Third Proportional to 13,838 and 21,463

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Solution

The third proportional to 13,838 and 21,463 is: 33,289.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,838 : 21,463 = 21,463 : x
  2. Step 2: Convert to fraction form
    13,838/21,463 = 21,463/x
  3. Step 3: Cross multiply
    13,838x = 21,463 × 21,463
  4. Step 4: Simplify right side
    13,838x = 460,660,369
  5. Step 5: Solve for x
    x = 460,660,369/13,838
  6. Step 6: Final answer
    x = 33,289.52

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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.