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Finding the Third Proportional to 13,540 and 19,462

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Solution

The third proportional to 13,540 and 19,462 is: 27,974.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,540 : 19,462 = 19,462 : x
  2. Step 2: Convert to fraction form
    13,540/19,462 = 19,462/x
  3. Step 3: Cross multiply
    13,540x = 19,462 × 19,462
  4. Step 4: Simplify right side
    13,540x = 378,769,444
  5. Step 5: Solve for x
    x = 378,769,444/13,540
  6. Step 6: Final answer
    x = 27,974.11

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.